Package org.apfloat

Class FixedPrecisionApcomplexHelper

java.lang.Object

org.apfloat.FixedPrecisionApcomplexHelper

Direct Known Subclasses:

FixedPrecisionApfloatHelper

public class FixedPrecisionApcomplexHelper
extends java.lang.Object

Fixed-precision mathematical functions for complex numbers.

All results of the mathematical operations are set to have the specified precision. Also all input arguments are set to the specified precision before the operation. If the specified precision is not infinite, this helper class also avoids InfiniteExpansionException e.g. in case where it would happen with ApcomplexMath.acos(Apcomplex.ZERO).

Since:

1.5

Version:

1.14.0

Field Summary

Fields

Modifier and Type	Field	Description
private long	precision

Constructor Summary

Constructors

Constructor	Description
FixedPrecisionApcomplexHelper(long precision)	Constructs an apcomplex fixed-precison helper with the specified precision.

Method Summary

Modifier and Type	Method	Description
Apfloat	abs(Apcomplex z)	Absolute value.
Apcomplex	acos(Apcomplex z)	Arc cosine.
Apcomplex	acosh(Apcomplex z)	Hyperbolic arc cosine.
Apcomplex	add(Apcomplex z, Apcomplex w)	Addition.
Apcomplex	agm(Apcomplex a, Apcomplex b)	Arithmetic-geometric mean.
Apcomplex	airyAi(Apcomplex z)	Airy function Ai.
Apcomplex	airyAiPrime(Apcomplex z)	Derivative of the Airy function Ai.
Apcomplex	airyBi(Apcomplex z)	Airy function Bi.
Apcomplex	airyBiPrime(Apcomplex z)	Derivative of the Airy function Bi.
Apcomplex[]	allRoots(Apcomplex z, int n)	All branches of a root.
Apfloat	arg(Apcomplex z)	Complex angle.
Apcomplex	asin(Apcomplex z)	Arc sine.
Apcomplex	asinh(Apcomplex z)	Hyperbolic arc sine.
Apcomplex	atan(Apcomplex z)	Arc tangent.
Apcomplex	atanh(Apcomplex z)	Hyperbolic arc tangent.
Apfloat	bernoulli(long n)	Bernoulli number.
Apfloat	bernoulli(long n, int radix)	Bernoulli number.
Apcomplex	bernoulliB(long n, Apcomplex z)	Bernoulli polynomial.
Apcomplex	besselI(Apcomplex ν, Apcomplex z)	Modified Bessel function of the first kind.
Apcomplex	besselJ(Apcomplex ν, Apcomplex z)	Bessel function of the first kind.
Apcomplex	besselK(Apcomplex ν, Apcomplex z)	Modified Bessel function of the second kind.
Apcomplex	besselY(Apcomplex ν, Apcomplex z)	Bessel function of the second kind.
Apcomplex	beta(Apcomplex a, Apcomplex b)	Beta function.
Apcomplex	beta(Apcomplex z, Apcomplex a, Apcomplex b)	Incomplete beta function.
Apcomplex	beta(Apcomplex z1, Apcomplex z2, Apcomplex a, Apcomplex b)	Generalized incomplete beta function.
Apfloat	binomial(long n, long k)	Binomial coefficient.
Apfloat	binomial(long n, long k, int radix)	Binomial coefficient.
Apcomplex	binomial(Apcomplex n, Apcomplex k)	Binomial coefficient.
Apfloat	catalan()	Catalan's constant G.
Apfloat	catalan(int radix)	Catalan's constant G.
Apcomplex	cbrt(Apcomplex z)	Cube root.
Apcomplex	chebyshevT(Apcomplex ν, Apcomplex z)	Chebyshev function of the first kind.
Apcomplex	chebyshevU(Apcomplex ν, Apcomplex z)	Chebyshev function of the second kind.
private Apcomplex	checkSmallLinear(Apcomplex z)
Apcomplex	conj(Apcomplex z)	Complex conjugate.
Apcomplex	cos(Apcomplex z)	Cosine.
Apcomplex	cosh(Apcomplex z)	Hyperbolic cosine.
Apcomplex	coshIntegral(Apcomplex z)	Hyperbolic cosine integral.
Apcomplex	cosIntegral(Apcomplex z)	Cosine integral.
Apcomplex	digamma(Apcomplex z)	Digamma function.
Apcomplex	divide(Apcomplex z, Apcomplex w)	Division.
Apfloat	e()	e.
Apfloat	e(int radix)	e.
Apcomplex	ellipticE(Apcomplex z)	Complete elliptic integral of the second kind.
Apcomplex	ellipticK(Apcomplex z)	Complete elliptic integral of the first kind.
Apcomplex	erf(Apcomplex z)	Error function.
Apcomplex	erfc(Apcomplex z)	Complementary error function.
Apcomplex	erfi(Apcomplex z)	Imaginary error function.
Apfloat	euler()	γ, the Euler-Mascheroni constant.
Apfloat	euler(int radix)	γ, the Euler-Mascheroni constant.
Apcomplex	eulerE(long n, Apcomplex z)	Euler polynomial.
Apcomplex	exp(Apcomplex z)	Exponential function.
Apcomplex	expIntegralE(Apcomplex ν, Apcomplex z)	Exponential integral E.
Apcomplex	expIntegralEi(Apcomplex z)	Exponential integral Ei.
Apcomplex	fibonacci(Apcomplex ν, Apcomplex z)	Fibonacci function.
Apcomplex	fresnelC(Apcomplex z)	Fresnel integral C.
Apcomplex	fresnelS(Apcomplex z)	Fresnel integral S.
Apcomplex	gamma(Apcomplex z)	Gamma function.
Apcomplex	gamma(Apcomplex a, Apcomplex z)	Incomplete gamma function.
Apcomplex	gamma(Apcomplex a, Apcomplex z0, Apcomplex z1)	Generalized incomplete gamma function.
Apcomplex	gegenbauerC(Apcomplex ν, Apcomplex z)	Renormalized Gegenbauer function.
Apcomplex	gegenbauerC(Apcomplex ν, Apcomplex λ, Apcomplex z)	Gegenbauer function.
Apfloat	glaisher()	The Glaisher-Kinkelin constant A.
Apfloat	glaisher(int radix)	The Glaisher-Kinkelin constant A.
Apcomplex	harmonicNumber(Apcomplex z)	Harmonic number.
Apcomplex	harmonicNumber(Apcomplex z, Apcomplex r)	Generalized harmonic number.
Apcomplex	hermiteH(Apcomplex ν, Apcomplex z)	Hermite function.
Apcomplex	hypergeometric0F1(Apcomplex a, Apcomplex z)	Confluent hypergeometric function 0F1.
Apcomplex	hypergeometric0F1Regularized(Apcomplex a, Apcomplex z)	Regularized confluent hypergeometric function 0F̃1.
Apcomplex	hypergeometric1F1(Apcomplex a, Apcomplex b, Apcomplex z)	Kummer confluent hypergeometric function 1F1.
Apcomplex	hypergeometric1F1Regularized(Apcomplex a, Apcomplex b, Apcomplex z)	Regularized Kummer confluent hypergeometric function 1F̃1.
Apcomplex	hypergeometric2F1(Apcomplex a, Apcomplex b, Apcomplex c, Apcomplex z)	Hypergeometric function 2F1.
Apcomplex	hypergeometric2F1Regularized(Apcomplex a, Apcomplex b, Apcomplex c, Apcomplex z)	Regularized hypergeometric function 2F̃1.
Apcomplex	hypergeometricU(Apcomplex a, Apcomplex b, Apcomplex z)	Tricomi's confluent hypergeometric function U.
Apfloat	imag(Apcomplex z)	Imaginary part.
Apcomplex	inverseRoot(Apcomplex z, long n)	Inverse root.
Apcomplex	inverseRoot(Apcomplex z, long n, long k)	Inverse root with branch.
Apcomplex	jacobiP(Apcomplex ν, Apcomplex a, Apcomplex b, Apcomplex z)	Jacobi function.
Apfloat	khinchin()	Khinchin's constant K.
Apfloat	khinchin(int radix)	Khinchin's constant K.
Apcomplex	laguerreL(Apcomplex ν, Apcomplex z)	Laguerre function.
Apcomplex	laguerreL(Apcomplex ν, Apcomplex λ, Apcomplex z)	Generalized Laguerre function.
Apcomplex	legendreP(Apcomplex ν, Apcomplex z)	Legendre function.
Apcomplex	legendreP(Apcomplex ν, Apcomplex μ, Apcomplex z)	Associated Legendre function of the first kind.
Apcomplex	legendreQ(Apcomplex ν, Apcomplex z)	Legendre function of the second kind.
Apcomplex	legendreQ(Apcomplex ν, Apcomplex μ, Apcomplex z)	Associated Legendre function of the second kind.
Apcomplex	log(Apcomplex z)	Natural logarithm.
Apcomplex	log(Apcomplex z, Apcomplex w)	Logarithm in specified base.
Apcomplex	logGamma(Apcomplex z)	Logarithm of the gamma function.
Apcomplex	logIntegral(Apcomplex z)	Logarithmic integral.
Apcomplex	logisticSigmoid(Apcomplex z)	Logistic sigmoid.
Apcomplex	multiply(Apcomplex z, Apcomplex w)	Multiplication.
Apcomplex	negate(Apcomplex z)	Negation.
Apfloat	norm(Apcomplex z)	Norm.
(package private) Apfloat	pi()
(package private) Apfloat	pi(int radix)
Apcomplex	pochhammer(Apcomplex z, Apcomplex n)	Pochhammer symbol.
Apcomplex	polygamma(long n, Apcomplex z)	Polygamma function.
Apcomplex	polylog(Apcomplex ν, Apcomplex z)	Polylogarithm.
Apcomplex	pow(Apcomplex z, long n)	Integer power.
Apcomplex	pow(Apcomplex z, Apcomplex w)	Power.
long	precision()	Returns the precision, which is used for the results.
Apcomplex	product(Apcomplex... z)	Product.
Apfloat	real(Apcomplex z)	Real part.
Apcomplex	root(Apcomplex z, long n)	Root.
Apcomplex	root(Apcomplex z, long n, long k)	Root with branch.
Apcomplex	scale(Apcomplex z, long scale)	Move the radix point.
private Apcomplex	setErfPrecision(Apcomplex z)
(package private) Apfloat	setErfPrecision(Apfloat x)
(package private) Apfloat	setExponentialPrecision(Apfloat x)
private Apcomplex	setExpTrigPrecision(Apcomplex z)
private Apcomplex	setGammaPrecision(Apcomplex z)
(package private) Apfloat	setGammaPrecision(Apfloat x)
private Apcomplex	setLogarithmicPrecision(Apcomplex z)
(package private) Apfloat	setLogarithmicPrecision(Apfloat x)
private Apcomplex	setPrecision(Apcomplex z)
private Apcomplex[]	setPrecision(Apcomplex[] z)
private Apcomplex	setTrigExpPrecision(Apcomplex z)
(package private) Apfloat	setTrigonometricPrecision(Apfloat x)
private Apcomplex	setZetaPrecision(Apcomplex z)
(package private) Apfloat	setZetaPrecision(Apfloat x)
Apcomplex	sin(Apcomplex z)	Sine.
Apcomplex	sinc(Apcomplex z)	Sinc.
Apcomplex	sinh(Apcomplex z)	Hyperbolic sine.
Apcomplex	sinhIntegral(Apcomplex z)	Hyperbolic sine integral.
Apcomplex	sinIntegral(Apcomplex z)	Sine integral.
Apcomplex	sphericalHarmonicY(Apcomplex λ, Apcomplex μ, Apcomplex ϑ, Apcomplex ϕ)	Spherical harmonic function.
Apcomplex	sqrt(Apcomplex z)	Square root.
Apcomplex	subtract(Apcomplex z, Apcomplex w)	Subtraction.
Apcomplex	sum(Apcomplex... z)	Sum.
Apcomplex	tan(Apcomplex z)	Tangent.
Apcomplex	tanh(Apcomplex z)	Hyperbolic tangent.
Apfloat	ulp(Apcomplex z)	Unit in the last place.
Apcomplex	valueOf(Apcomplex z)	Returns the value with the specified precision.
(package private) Apfloat	valueOf(Apfloat x)
Apcomplex	w(Apcomplex z)	Lambert W function.
Apcomplex	w(Apcomplex z, long k)	Lambert W function for the specified branch.
Apcomplex	zeta(Apcomplex s)	Riemann zeta function.
Apcomplex	zeta(Apcomplex s, Apcomplex a)	Hurwitz zeta function.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

precision

private long precision

Constructor Detail

FixedPrecisionApcomplexHelper

public FixedPrecisionApcomplexHelper(long precision)
                              throws java.lang.IllegalArgumentException

Constructs an apcomplex fixed-precison helper with the specified precision. The results of all mathematical operations are set to the specified precision.

Parameters:

precision - The precision of the results.

Throws:

java.lang.IllegalArgumentException - In case the precision is invalid.

Method Detail

valueOf

public Apcomplex valueOf(Apcomplex z)
                  throws ApfloatRuntimeException

Returns the value with the specified precision.

Parameters:

z - The value.

Returns:

The value with to the specified precision.

Throws:

ApfloatRuntimeException

negate

public Apcomplex negate(Apcomplex z)
                 throws ApfloatRuntimeException

Negation.

Parameters:

z - The value to negate.

Returns:

-z.

Throws:

ApfloatRuntimeException

conj

public Apcomplex conj(Apcomplex z)
               throws ApfloatRuntimeException

Complex conjugate.

Parameters:

z - The operand.

Returns:

x - i y where z is x + i y.

Throws:

ApfloatRuntimeException

add

public Apcomplex add(Apcomplex z,
                     Apcomplex w)
              throws ApfloatRuntimeException

Addition.

Parameters:

z - The first operand.

w - The second operand.

Returns:

z + w.

Throws:

ApfloatRuntimeException

subtract

public Apcomplex subtract(Apcomplex z,
                          Apcomplex w)
                   throws ApfloatRuntimeException

Subtraction.

Parameters:

z - The first operand.

w - The second operand.

Returns:

z - w.

Throws:

ApfloatRuntimeException

multiply

public Apcomplex multiply(Apcomplex z,
                          Apcomplex w)
                   throws ApfloatRuntimeException

Multiplication.

Parameters:

z - The first operand.

w - The second operand.

Returns:

z * w.

Throws:

ApfloatRuntimeException

divide

public Apcomplex divide(Apcomplex z,
                        Apcomplex w)
                 throws java.lang.ArithmeticException,
                        ApfloatRuntimeException

Division.

Parameters:

z - The first operand.

w - The second operand.

Returns:

z / w.

Throws:

java.lang.ArithmeticException - If w is zero.

ApfloatRuntimeException

pow

public Apcomplex pow(Apcomplex z,
                     Apcomplex w)
              throws java.lang.ArithmeticException,
                     ApfloatRuntimeException

Power.

Parameters:

z - The first operand.

w - The second operand.

Returns:

zw.

Throws:

java.lang.ArithmeticException - If z and w are zero.

ApfloatRuntimeException

pow

public Apcomplex pow(Apcomplex z,
                     long n)
              throws java.lang.ArithmeticException,
                     ApfloatRuntimeException

Integer power.

Parameters:

z - The first operand.

n - The first operand.

Returns:

zn.

Throws:

java.lang.ArithmeticException - If z and n are zero, or z is zero and n is negative.

ApfloatRuntimeException

arg

public Apfloat arg(Apcomplex z)
            throws java.lang.ArithmeticException,
                   ApfloatRuntimeException

Complex angle.

Parameters:

z - The operand.

Returns:

The angle of z on the complex plane.

Throws:

java.lang.ArithmeticException - If z is zero.

ApfloatRuntimeException

imag

public Apfloat imag(Apcomplex z)

Imaginary part.

Parameters:

z - The operand.

Returns:

The imaginary part of z.

real

public Apfloat real(Apcomplex z)

Real part.

Parameters:

z - The operand.

Returns:

The real part of z.

abs

public Apfloat abs(Apcomplex z)
            throws ApfloatRuntimeException

Absolute value.

Parameters:

z - The operand.

Returns:

The absolute value of z.

Throws:

ApfloatRuntimeException

norm

public Apfloat norm(Apcomplex z)
             throws ApfloatRuntimeException

Norm.

Parameters:

z - The operand.

Returns:

x2 + y2 where z is x + i y.

Throws:

ApfloatRuntimeException

acos

public Apcomplex acos(Apcomplex z)
               throws ApfloatRuntimeException

Arc cosine.

Parameters:

z - The operand.

Returns:

The arc cosine of z.

Throws:

ApfloatRuntimeException

acosh

public Apcomplex acosh(Apcomplex z)
                throws ApfloatRuntimeException

Hyperbolic arc cosine.

Parameters:

z - The operand.

Returns:

The hyperbolic arc cosine of z.

Throws:

ApfloatRuntimeException

asin

public Apcomplex asin(Apcomplex z)
               throws ApfloatRuntimeException

Arc sine.

Parameters:

z - The operand.

Returns:

The arc sine of z.

Throws:

ApfloatRuntimeException

asinh

public Apcomplex asinh(Apcomplex z)
                throws ApfloatRuntimeException

Hyperbolic arc sine.

Parameters:

z - The operand.

Returns:

The hyperbolic arc sine of z.

Throws:

ApfloatRuntimeException

atan

public Apcomplex atan(Apcomplex z)
               throws ApfloatRuntimeException

Arc tangent.

Parameters:

z - The operand.

Returns:

The arc tangent of z.

Throws:

java.lang.ArithmeticException - If z is i.

ApfloatRuntimeException

atanh

public Apcomplex atanh(Apcomplex z)
                throws java.lang.ArithmeticException,
                       ApfloatRuntimeException

Hyperbolic arc tangent.

Parameters:

z - The operand.

Returns:

The hyperbolic arc tangent of z.

Throws:

java.lang.ArithmeticException - If z is 1 or -1.

ApfloatRuntimeException

cbrt

public Apcomplex cbrt(Apcomplex z)
               throws ApfloatRuntimeException

Cube root.

Parameters:

z - The operand.

Returns:

The cube root of z.

Throws:

ApfloatRuntimeException

cos

public Apcomplex cos(Apcomplex z)
              throws ApfloatRuntimeException

Cosine.

Parameters:

z - The operand.

Returns:

The cosine of z.

Throws:

ApfloatRuntimeException

cosh

public Apcomplex cosh(Apcomplex z)
               throws ApfloatRuntimeException

Hyperbolic cosine.

Parameters:

z - The operand.

Returns:

The hyperbolic cosine of z.

Throws:

ApfloatRuntimeException

exp

public Apcomplex exp(Apcomplex z)
              throws ApfloatRuntimeException

Exponential function.

Parameters:

z - The operand.

Returns:

ez.

Throws:

ApfloatRuntimeException

log

public Apcomplex log(Apcomplex z)
              throws java.lang.ArithmeticException,
                     ApfloatRuntimeException

Natural logarithm.

Parameters:

z - The operand.

Returns:

The natural logarithm of z.

Throws:

java.lang.ArithmeticException - If z is zero.

ApfloatRuntimeException

log

public Apcomplex log(Apcomplex z,
                     Apcomplex w)
              throws java.lang.ArithmeticException,
                     ApfloatRuntimeException

Logarithm in specified base.

Parameters:

z - The operand.

w - The base.

Returns:

The base-w logarithm of z.

Throws:

java.lang.ArithmeticException - If z or w is zero.

ApfloatRuntimeException

Since:

1.6

sin

public Apcomplex sin(Apcomplex z)
              throws ApfloatRuntimeException

Sine.

Parameters:

z - The operand.

Returns:

The sine of z.

Throws:

ApfloatRuntimeException

sinh

public Apcomplex sinh(Apcomplex z)
               throws ApfloatRuntimeException

Hyperbolic sine.

Parameters:

z - The operand.

Returns:

The hyperbolic sine of z.

Throws:

ApfloatRuntimeException

sqrt

public Apcomplex sqrt(Apcomplex z)
               throws ApfloatRuntimeException

Square root.

Parameters:

z - The operand.

Returns:

The square root of z.

Throws:

ApfloatRuntimeException

tan

public Apcomplex tan(Apcomplex z)
              throws java.lang.ArithmeticException,
                     ApfloatRuntimeException

Tangent.

Parameters:

z - The operand.

Returns:

The tangent of z.

Throws:

java.lang.ArithmeticException - If z is π/2 + n π where n is an integer.

ApfloatRuntimeException

tanh

public Apcomplex tanh(Apcomplex z)
               throws java.lang.ArithmeticException,
                      ApfloatRuntimeException

Hyperbolic tangent.

Parameters:

z - The operand.

Returns:

The hyperbolic tangent of z.

Throws:

java.lang.ArithmeticException - If z is i (π/2 + n π) where n is an integer.

ApfloatRuntimeException

sinc

public Apcomplex sinc(Apcomplex z)
               throws ApfloatRuntimeException

Sinc.

Parameters:

z - The argument.

Returns:

sinc(z)

Throws:

ApfloatRuntimeException

Since:

1.14.0

agm

public Apcomplex agm(Apcomplex a,
                     Apcomplex b)
              throws ApfloatRuntimeException

Arithmetic-geometric mean.

Parameters:

a - The first operand.

b - The first operand.

Returns:

The arithmetic-geometric mean of a and b.

Throws:

ApfloatRuntimeException

inverseRoot

public Apcomplex inverseRoot(Apcomplex z,
                             long n)
                      throws java.lang.ArithmeticException,
                             ApfloatRuntimeException

Inverse root.

Parameters:

z - The operand.

n - Which inverse root to take.

Returns:

z-1/n.

Throws:

java.lang.ArithmeticException - If z or n is zero.

ApfloatRuntimeException

inverseRoot

public Apcomplex inverseRoot(Apcomplex z,
                             long n,
                             long k)
                      throws java.lang.ArithmeticException,
                             ApfloatRuntimeException

Inverse root with branch.

Parameters:

z - The operand.

n - Which inverse root to take.

k - Which branch to take.

Returns:

z-1/ne-i2πk/n.

Throws:

java.lang.ArithmeticException - If z or n is zero.

ApfloatRuntimeException

root

public Apcomplex root(Apcomplex z,
                      long n)
               throws java.lang.ArithmeticException,
                      ApfloatRuntimeException

Root.

Parameters:

z - The operand.

n - Which root to take.

Returns:

z1/n.

Throws:

java.lang.ArithmeticException - If n is zero, or z is zero and n is negative.

ApfloatRuntimeException

root

public Apcomplex root(Apcomplex z,
                      long n,
                      long k)
               throws java.lang.ArithmeticException,
                      ApfloatRuntimeException

Root with branch.

Parameters:

z - The operand.

n - Which root to take.

k - Which branch to take.

Returns:

z1/nei2πsk/n where s is the signum of the imaginary part of z.

Throws:

java.lang.ArithmeticException - If n is zero, or z is zero and n is negative.

ApfloatRuntimeException

allRoots

public Apcomplex[] allRoots(Apcomplex z,
                            int n)
                     throws java.lang.ArithmeticException,
                            ApfloatRuntimeException

All branches of a root.

Parameters:

z - The operand.

n - Which root to take.

Returns:

z1/n.

Throws:

java.lang.ArithmeticException - If n is zero, or z is zero and n is negative.

ApfloatRuntimeException

scale

public Apcomplex scale(Apcomplex z,
                       long scale)
                throws ApfloatRuntimeException

Move the radix point.

Parameters:

z - The operand.

scale - The amount to move the radix point.

Returns:

z * z.radix()scale.

Throws:

ApfloatRuntimeException

w

public Apcomplex w(Apcomplex z)
            throws ApfloatRuntimeException

Lambert W function.

Parameters:

z - The operand.

Returns:

W0(z).

Throws:

ApfloatRuntimeException

Since:

1.8.0

w

public Apcomplex w(Apcomplex z,
                   long k)
            throws ApfloatRuntimeException

Lambert W function for the specified branch.

Parameters:

z - The operand.

k - The branch.

Returns:

Wk(z).

Throws:

ApfloatRuntimeException

Since:

1.8.0

product

public Apcomplex product(Apcomplex... z)
                  throws ApfloatRuntimeException

Product.

Parameters:

z - The operand(s).

Returns:

The product of the operands.

Throws:

ApfloatRuntimeException

sum

public Apcomplex sum(Apcomplex... z)
              throws ApfloatRuntimeException

Sum.

Parameters:

z - The operand(s).

Returns:

The sum of the operands.

Throws:

ApfloatRuntimeException

e

public Apfloat e()
          throws ApfloatRuntimeException

e.

Returns:

e.

Throws:

ApfloatRuntimeException

Since:

1.11.0

e

public Apfloat e(int radix)
          throws java.lang.NumberFormatException,
                 ApfloatRuntimeException

e.

Parameters:

radix - The radix of the result.

Returns:

e.

Throws:

java.lang.NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

Since:

1.11.0

euler

public Apfloat euler()
              throws ApfloatRuntimeException

γ, the Euler-Mascheroni constant.

Returns:

γ.

Throws:

ApfloatRuntimeException

Since:

1.11.0

euler

public Apfloat euler(int radix)
              throws java.lang.NumberFormatException,
                     ApfloatRuntimeException

γ, the Euler-Mascheroni constant.

Parameters:

radix - The radix of the result.

Returns:

γ.

Throws:

java.lang.NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

Since:

1.11.0

catalan

public Apfloat catalan()
                throws ApfloatRuntimeException

Catalan's constant G.

Returns:

G.

Throws:

ApfloatRuntimeException

Since:

1.11.0

catalan

public Apfloat catalan(int radix)
                throws java.lang.NumberFormatException,
                       ApfloatRuntimeException

Catalan's constant G.

Parameters:

radix - The radix of the result.

Returns:

G.

Throws:

java.lang.NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

Since:

1.11.0

glaisher

public Apfloat glaisher()
                 throws ApfloatRuntimeException

The Glaisher-Kinkelin constant A.

Returns:

A.

Throws:

ApfloatRuntimeException

Since:

1.11.0

glaisher

public Apfloat glaisher(int radix)
                 throws java.lang.NumberFormatException,
                        ApfloatRuntimeException

The Glaisher-Kinkelin constant A.

Parameters:

radix - The radix of the result.

Returns:

A.

Throws:

java.lang.NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

Since:

1.11.0

khinchin

public Apfloat khinchin()
                 throws ApfloatRuntimeException

Khinchin's constant K.

Returns:

K.

Throws:

ApfloatRuntimeException

Since:

1.11.0

khinchin

public Apfloat khinchin(int radix)
                 throws java.lang.NumberFormatException,
                        ApfloatRuntimeException

Khinchin's constant K.

Parameters:

radix - The radix of the result.

Returns:

K.

Throws:

java.lang.NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

Since:

1.11.0

gamma

public Apcomplex gamma(Apcomplex z)
                throws java.lang.ArithmeticException,
                       ApfloatRuntimeException

Gamma function.

Parameters:

z - The operand.

Returns:

Γ(z).

Throws:

java.lang.ArithmeticException - If z is a nonpositive integer.

ApfloatRuntimeException

Since:

1.9.0

gamma

public Apcomplex gamma(Apcomplex a,
                       Apcomplex z)
                throws java.lang.ArithmeticException,
                       ApfloatRuntimeException

Incomplete gamma function.

Parameters:

a - The first operand.

z - The second operand.

Returns:

Γ(a, z).

Throws:

java.lang.ArithmeticException - If a is a nonpositive integer and z is zero.

ApfloatRuntimeException

Since:

1.10.0

gamma

public Apcomplex gamma(Apcomplex a,
                       Apcomplex z0,
                       Apcomplex z1)
                throws java.lang.ArithmeticException,
                       ApfloatRuntimeException

Generalized incomplete gamma function.

Parameters:

a - The first operand.

z0 - The second operand.

z1 - The third operand.

Returns:

Γ(a, z0) - Γ(a, z1).

Throws:

java.lang.ArithmeticException - If a is a nonpositive integer and either z0 or z1 is zero.

ApfloatRuntimeException

Since:

1.10.0

logGamma

public Apcomplex logGamma(Apcomplex z)
                   throws java.lang.ArithmeticException,
                          ApfloatRuntimeException

Logarithm of the gamma function.

Parameters:

z - The argument.

Returns:

logΓ(z)

Throws:

java.lang.ArithmeticException - If z is a nonpositive integer.

ApfloatRuntimeException

Since:

1.11.0

digamma

public Apcomplex digamma(Apcomplex z)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException

Digamma function.

Parameters:

z - The argument.

Returns:

ψ(z)

Throws:

java.lang.ArithmeticException - If z is a nonpositive integer.

ApfloatRuntimeException

Since:

1.11.0

polygamma

public Apcomplex polygamma(long n,
                           Apcomplex z)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Polygamma function.

Parameters:

n - The order.

z - The argument.

Returns:

ψ(n)(z)

Throws:

java.lang.ArithmeticException - If n is negative or z is a nonpositive integer.

ApfloatRuntimeException

Since:

1.13.0

beta

public Apcomplex beta(Apcomplex a,
                      Apcomplex b)
               throws java.lang.ArithmeticException,
                      ApfloatRuntimeException

Beta function.

Parameters:

a - The first argument.

b - The second argument.

Returns:

B(a, b)

Throws:

java.lang.ArithmeticException - If a or b is a nonpositive integer but a + b is not. Also if both a and b are nonpositive integers.

ApfloatRuntimeException

Since:

1.13.0

beta

public Apcomplex beta(Apcomplex z,
                      Apcomplex a,
                      Apcomplex b)
               throws java.lang.ArithmeticException,
                      ApfloatRuntimeException

Incomplete beta function.

Parameters:

z - The first argument.

a - The second argument.

b - The third argument.

Returns:

B_z(a, b)

Throws:

java.lang.ArithmeticException - If a is a nonpositive integer or z is zero and a has nonpositive real part.

ApfloatRuntimeException

Since:

1.13.0

beta

public Apcomplex beta(Apcomplex z1,
                      Apcomplex z2,
                      Apcomplex a,
                      Apcomplex b)
               throws java.lang.ArithmeticException,
                      ApfloatRuntimeException

Generalized incomplete beta function.

Parameters:

z1 - The first argument.

z2 - The second argument.

a - The third argument.

b - The fourth argument.

Returns:

B_{(z1, z2)}(a, b)

Throws:

java.lang.ArithmeticException - If a is a nonpositive integer or z1 or z2 is zero and a has nonpositive real part.

ApfloatRuntimeException

Since:

1.13.0

pochhammer

public Apcomplex pochhammer(Apcomplex z,
                            Apcomplex n)
                     throws java.lang.ArithmeticException,
                            ApfloatRuntimeException

Pochhammer symbol.

Parameters:

z - The first argument.

n - The second argument.

Returns:

(z)n

Throws:

java.lang.ArithmeticException - If z + n is a nonpositive integer but z is not.

ApfloatRuntimeException

Since:

1.13.0

binomial

public Apfloat binomial(long n,
                        long k)
                 throws java.lang.ArithmeticException,
                        ApfloatRuntimeException

Binomial coefficient.

Parameters:

n - The argument.

k - The argument.

Returns:

The binomial coefficient.

Throws:

java.lang.ArithmeticException - If n or k is negative.

ApfloatRuntimeException

Since:

1.11.0

binomial

public Apfloat binomial(long n,
                        long k,
                        int radix)
                 throws java.lang.ArithmeticException,
                        java.lang.NumberFormatException,
                        ApfloatRuntimeException

Binomial coefficient.

Parameters:

n - The argument.

k - The argument.

radix - The radix.

Returns:

The binomial coefficient.

Throws:

java.lang.ArithmeticException - If n or k is negative.

java.lang.NumberFormatException - If the radix is not valid.

ApfloatRuntimeException

Since:

1.11.0

binomial

public Apcomplex binomial(Apcomplex n,
                          Apcomplex k)
                   throws java.lang.ArithmeticException,
                          ApfloatRuntimeException

Binomial coefficient.

Parameters:

n - The argument.

k - The argument.

Returns:

The binomial coefficient.

Throws:

java.lang.ArithmeticException - If n, k or n - k is a nonpositive integer.

ApfloatRuntimeException

Since:

1.11.0

bernoulli

public Apfloat bernoulli(long n)
                  throws java.lang.IllegalArgumentException,
                         ApfloatRuntimeException

Bernoulli number.

Parameters:

n - The argument.

Returns:

Bn

Throws:

java.lang.IllegalArgumentException - If n < 0.

ApfloatRuntimeException

Since:

1.11.0

bernoulli

public Apfloat bernoulli(long n,
                         int radix)
                  throws java.lang.IllegalArgumentException,
                         java.lang.NumberFormatException,
                         ApfloatRuntimeException

Bernoulli number.

Parameters:

n - The argument.

radix - The radix.

Returns:

Bn

Throws:

java.lang.IllegalArgumentException - If n < 0.

java.lang.NumberFormatException - If the radix is not valid.

ApfloatRuntimeException

Since:

1.11.0

zeta

public Apcomplex zeta(Apcomplex s)
               throws java.lang.ArithmeticException,
                      ApfloatRuntimeException

Riemann zeta function.

Parameters:

s - The argument.

Returns:

ζ(s)

Throws:

java.lang.ArithmeticException - If s is 1.

ApfloatRuntimeException

Since:

1.11.0

zeta

public Apcomplex zeta(Apcomplex s,
                      Apcomplex a)
               throws java.lang.ArithmeticException,
                      ApfloatRuntimeException

Hurwitz zeta function.

Parameters:

s - The first argument.

a - The second argument.

Returns:

ζ(s, a)

Throws:

java.lang.ArithmeticException - If s is 1 or if a is a nonpositive integer.

ApfloatRuntimeException

Since:

1.11.0

hypergeometric0F1

public Apcomplex hypergeometric0F1(Apcomplex a,
                                   Apcomplex z)
                            throws java.lang.ArithmeticException,
                                   ApfloatRuntimeException

Confluent hypergeometric function ₀F₁.

Parameters:

a - The first argument.

z - The second argument.

Returns:

₀F₁(; a; z)

Throws:

java.lang.ArithmeticException - If the function value is not finite.

ApfloatRuntimeException

Since:

1.11.0

hypergeometric0F1Regularized

public Apcomplex hypergeometric0F1Regularized(Apcomplex a,
                                              Apcomplex z)
                                       throws ApfloatRuntimeException

Regularized confluent hypergeometric function ₀F̃₁.

Parameters:

a - The first argument.

z - The second argument.

Returns:

₀F̃₁(; a; z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

hypergeometric1F1

public Apcomplex hypergeometric1F1(Apcomplex a,
                                   Apcomplex b,
                                   Apcomplex z)
                            throws java.lang.ArithmeticException,
                                   ApfloatRuntimeException

Kummer confluent hypergeometric function ₁F₁.

Parameters:

a - The first argument.

b - The second argument.

z - The third argument.

Returns:

₁F₁(a; b; z)

Throws:

java.lang.ArithmeticException - If the function value is not finite.

ApfloatRuntimeException

Since:

1.11.0

hypergeometric1F1Regularized

public Apcomplex hypergeometric1F1Regularized(Apcomplex a,
                                              Apcomplex b,
                                              Apcomplex z)
                                       throws ApfloatRuntimeException

Regularized Kummer confluent hypergeometric function ₁F̃₁.

Parameters:

a - The first argument.

b - The second argument.

z - The third argument.

Returns:

₁F̃₁(a; b; z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

hypergeometric2F1

public Apcomplex hypergeometric2F1(Apcomplex a,
                                   Apcomplex b,
                                   Apcomplex c,
                                   Apcomplex z)
                            throws java.lang.ArithmeticException,
                                   ApfloatRuntimeException

Hypergeometric function ₂F₁.

Parameters:

a - The first argument.

b - The second argument.

c - The third argument.

z - The fourth argument.

Returns:

₂F₁(a, b; c; z)

Throws:

java.lang.ArithmeticException - If the function value is not finite.

ApfloatRuntimeException

Since:

1.11.0

hypergeometric2F1Regularized

public Apcomplex hypergeometric2F1Regularized(Apcomplex a,
                                              Apcomplex b,
                                              Apcomplex c,
                                              Apcomplex z)
                                       throws ApfloatRuntimeException

Regularized hypergeometric function ₂F̃₁.

Parameters:

a - The first argument.

b - The second argument.

c - The third argument.

z - The fourth argument.

Returns:

₂F̃₁(a, b; c; z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

hypergeometricU

public Apcomplex hypergeometricU(Apcomplex a,
                                 Apcomplex b,
                                 Apcomplex z)
                          throws java.lang.ArithmeticException,
                                 ApfloatRuntimeException

Tricomi's confluent hypergeometric function U.

Parameters:

a - The first argument.

b - The second argument.

z - The third argument.

Returns:

U(a, b, z)

Throws:

java.lang.ArithmeticException - If the result is not finite.

ApfloatRuntimeException

Since:

1.13.0

erf

public Apcomplex erf(Apcomplex z)
              throws ApfloatRuntimeException

Error function.

Parameters:

z - The argument.

Returns:

erf(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

erfc

public Apcomplex erfc(Apcomplex z)
               throws ApfloatRuntimeException

Complementary error function.

Parameters:

z - The argument.

Returns:

erfc(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

erfi

public Apcomplex erfi(Apcomplex z)
               throws ApfloatRuntimeException

Imaginary error function.

Parameters:

z - The argument.

Returns:

erfi(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

fresnelS

public Apcomplex fresnelS(Apcomplex z)
                   throws ApfloatRuntimeException

Fresnel integral S.

Parameters:

z - The argument.

Returns:

S(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

fresnelC

public Apcomplex fresnelC(Apcomplex z)
                   throws ApfloatRuntimeException

Fresnel integral C.

Parameters:

z - The argument.

Returns:

C(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

expIntegralE

public Apcomplex expIntegralE(Apcomplex ν,
                              Apcomplex z)
                       throws java.lang.ArithmeticException,
                              ApfloatRuntimeException

Exponential integral E.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

E_ν(z)

Throws:

java.lang.ArithmeticException - If real part of ν is < 0 and z is zero.

ApfloatRuntimeException

Since:

1.13.0

expIntegralEi

public Apcomplex expIntegralEi(Apcomplex z)
                        throws java.lang.ArithmeticException,
                               ApfloatRuntimeException

Exponential integral Ei.

Parameters:

z - The argument.

Returns:

Ei(z)

Throws:

java.lang.ArithmeticException - If z is zero.

ApfloatRuntimeException

Since:

1.13.0

logIntegral

public Apcomplex logIntegral(Apcomplex z)
                      throws java.lang.ArithmeticException,
                             ApfloatRuntimeException

Logarithmic integral.

Parameters:

z - The argument.

Returns:

li(z)

Throws:

java.lang.ArithmeticException - If z is zero.

ApfloatRuntimeException

Since:

1.13.0

sinIntegral

public Apcomplex sinIntegral(Apcomplex z)
                      throws ApfloatRuntimeException

Sine integral.

Parameters:

z - The argument.

Returns:

Si(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

cosIntegral

public Apcomplex cosIntegral(Apcomplex z)
                      throws java.lang.ArithmeticException,
                             ApfloatRuntimeException

Cosine integral.

Parameters:

z - The argument.

Returns:

Ci(z)

Throws:

java.lang.ArithmeticException - If z is zero.

ApfloatRuntimeException

Since:

1.13.0

sinhIntegral

public Apcomplex sinhIntegral(Apcomplex z)
                       throws ApfloatRuntimeException

Hyperbolic sine integral.

Parameters:

z - The argument.

Returns:

Shi(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

coshIntegral

public Apcomplex coshIntegral(Apcomplex z)
                       throws java.lang.ArithmeticException,
                              ApfloatRuntimeException

Hyperbolic cosine integral.

Parameters:

z - The argument.

Returns:

Chi(z)

Throws:

java.lang.ArithmeticException - If z is zero.

ApfloatRuntimeException

Since:

1.13.0

airyAi

public Apcomplex airyAi(Apcomplex z)
                 throws ApfloatRuntimeException

Airy function Ai.

Parameters:

z - The argument.

Returns:

Ai(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

airyAiPrime

public Apcomplex airyAiPrime(Apcomplex z)
                      throws ApfloatRuntimeException

Derivative of the Airy function Ai.

Parameters:

z - The argument.

Returns:

Ai′(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

airyBi

public Apcomplex airyBi(Apcomplex z)
                 throws ApfloatRuntimeException

Airy function Bi.

Parameters:

z - The argument.

Returns:

Bi(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

airyBiPrime

public Apcomplex airyBiPrime(Apcomplex z)
                      throws ApfloatRuntimeException

Derivative of the Airy function Bi.

Parameters:

z - The argument.

Returns:

Bi′(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

besselJ

public Apcomplex besselJ(Apcomplex ν,
                         Apcomplex z)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException

Bessel function of the first kind.

Parameters:

\u03bd - The order.

z - The argument.

Returns:

J_ν(z)

Throws:

java.lang.ArithmeticException - If the real part of ν is < 0 and ν is not an integer and z is zero. Also if the real part of ν is zero but the imaginary part is not, and z is zero.

ApfloatRuntimeException

Since:

1.13.0

besselI

public Apcomplex besselI(Apcomplex ν,
                         Apcomplex z)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException

Modified Bessel function of the first kind.

Parameters:

\u03bd - The order.

z - The argument.

Returns:

I_ν(z)

Throws:

java.lang.ArithmeticException - If the real part of ν is < 0 and ν is not an integer and z is zero. Also if the real part of ν is zero but the imaginary part is not, and z is zero.

ApfloatRuntimeException

Since:

1.13.0

besselY

public Apcomplex besselY(Apcomplex ν,
                         Apcomplex z)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException

Bessel function of the second kind.

Parameters:

\u03bd - The order.

z - The argument.

Returns:

Y_ν(z)

Throws:

java.lang.ArithmeticException - If z is zero.

ApfloatRuntimeException

Since:

1.13.0

besselK

public Apcomplex besselK(Apcomplex ν,
                         Apcomplex z)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException

Modified Bessel function of the second kind.

Parameters:

\u03bd - The order.

z - The argument.

Returns:

K_ν(z)

Throws:

java.lang.ArithmeticException - If z is zero.

ApfloatRuntimeException

Since:

1.13.0

ellipticK

public Apcomplex ellipticK(Apcomplex z)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Complete elliptic integral of the first kind.

Parameters:

z - The argument.

Returns:

K(z)

Throws:

java.lang.ArithmeticException - If z is one.

ApfloatRuntimeException

Since:

1.13.0

ellipticE

public Apcomplex ellipticE(Apcomplex z)
                    throws ApfloatRuntimeException

Complete elliptic integral of the second kind.

Parameters:

z - The argument.

Returns:

E(z)

Throws:

ApfloatRuntimeException

Since:

1.13.0

hermiteH

public Apcomplex hermiteH(Apcomplex ν,
                          Apcomplex z)
                   throws ApfloatRuntimeException

Hermite function.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

H_ν(z)

Throws:

ApfloatRuntimeException

Since:

1.14.0

laguerreL

public Apcomplex laguerreL(Apcomplex ν,
                           Apcomplex z)
                    throws ApfloatRuntimeException

Laguerre function.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

L_ν(z)

Throws:

ApfloatRuntimeException

Since:

1.14.0

laguerreL

public Apcomplex laguerreL(Apcomplex ν,
                           Apcomplex λ,
                           Apcomplex z)
                    throws ApfloatRuntimeException

Generalized Laguerre function.

Parameters:

\u03bd - The first argument.

\u03bb - The second argument.

z - The third argument.

Returns:

L_ν^λ(z)

Throws:

ApfloatRuntimeException

Since:

1.14.0

legendreP

public Apcomplex legendreP(Apcomplex ν,
                           Apcomplex z)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Legendre function.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

P_ν(z)

Throws:

java.lang.ArithmeticException - If ν is not an integer and z is -1.

ApfloatRuntimeException

Since:

1.14.0

legendreP

public Apcomplex legendreP(Apcomplex ν,
                           Apcomplex μ,
                           Apcomplex z)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Associated Legendre function of the first kind.

Parameters:

\u03bd - The first argument.

\u03bc - The second argument.

z - The third argument.

Returns:

P_ν^μ(z)

Throws:

java.lang.ArithmeticException - If ν is not an integer and z is -1.

ApfloatRuntimeException

Since:

1.14.0

legendreQ

public Apcomplex legendreQ(Apcomplex ν,
                           Apcomplex z)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Legendre function of the second kind.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

Q_ν(z)

Throws:

java.lang.ArithmeticException - If z is 1 or -1.

ApfloatRuntimeException

Since:

1.14.0

legendreQ

public Apcomplex legendreQ(Apcomplex ν,
                           Apcomplex μ,
                           Apcomplex z)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Associated Legendre function of the second kind.

Parameters:

\u03bd - The first argument.

\u03bc - The second argument.

z - The third argument.

Returns:

Q_ν^μ(z)

Throws:

java.lang.ArithmeticException - If z is 1 or -1.

ApfloatRuntimeException

Since:

1.14.0

sphericalHarmonicY

public Apcomplex sphericalHarmonicY(Apcomplex λ,
                                    Apcomplex μ,
                                    Apcomplex ϑ,
                                    Apcomplex ϕ)
                             throws java.lang.ArithmeticException,
                                    ApfloatRuntimeException

Spherical harmonic function.

Parameters:

\u03bb - The first argument.

\u03bc - The second argument.

\u03d1 - The third argument.

\u03d5 - The fourth argument.

Returns:

Y_λ^μ(ϑ, φ)

Throws:

java.lang.ArithmeticException - If ϑ is π plus a multiple of 2 π and μ is not an integer and has a negative real part, or if λ - μ is a negative integer.

ApfloatRuntimeException

Since:

1.14.0

chebyshevT

public Apcomplex chebyshevT(Apcomplex ν,
                            Apcomplex z)
                     throws ApfloatRuntimeException

Chebyshev function of the first kind.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

T_ν(z)

Throws:

ApfloatRuntimeException

Since:

1.14.0

chebyshevU

public Apcomplex chebyshevU(Apcomplex ν,
                            Apcomplex z)
                     throws java.lang.ArithmeticException,
                            ApfloatRuntimeException

Chebyshev function of the second kind.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

U_ν(z)

Throws:

java.lang.ArithmeticException - If z is -1 and ν is not an integer.

ApfloatRuntimeException

Since:

1.14.0

gegenbauerC

public Apcomplex gegenbauerC(Apcomplex ν,
                             Apcomplex z)
                      throws java.lang.ArithmeticException,
                             ApfloatRuntimeException

Renormalized Gegenbauer function.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

C_ν⁽⁰⁾(z)

Throws:

java.lang.ArithmeticException - If ν is zero.

ApfloatRuntimeException

Since:

1.14.0

gegenbauerC

public Apcomplex gegenbauerC(Apcomplex ν,
                             Apcomplex λ,
                             Apcomplex z)
                      throws java.lang.ArithmeticException,
                             ApfloatRuntimeException

Gegenbauer function.

Parameters:

\u03bd - The first argument.

\u03bb - The second argument.

z - The third argument.

Returns:

C_ν^λ(z)

Throws:

java.lang.ArithmeticException - If z is -1 and real part of λ is > 1/2. Also if z is -1 and λ is 1/2 and ν is not an integer.

ApfloatRuntimeException

Since:

1.14.0

jacobiP

public Apcomplex jacobiP(Apcomplex ν,
                         Apcomplex a,
                         Apcomplex b,
                         Apcomplex z)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException

Jacobi function.

Parameters:

\u03bd - The first argument.

a - The second argument.

b - The third argument.

z - The fourth argument.

Returns:

P_ν^(a,b)(z)

Throws:

java.lang.ArithmeticException - If z is -1 and real part of b is > 0 and ν is not a positive integer. Also if ν + a is a negative integer and ν is not an integer.

ApfloatRuntimeException

Since:

1.14.0

fibonacci

public Apcomplex fibonacci(Apcomplex ν,
                           Apcomplex z)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException

Fibonacci function.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

F_ν(z)

Throws:

java.lang.ArithmeticException - If z is -1 and ν is not an integer.

ApfloatRuntimeException

Since:

1.14.0

eulerE

public Apcomplex eulerE(long n,
                        Apcomplex z)
                 throws java.lang.IllegalArgumentException,
                        ApfloatRuntimeException

Euler polynomial.

Parameters:

n - The first argument.

z - The second argument.

Returns:

E_n(z)

Throws:

java.lang.IllegalArgumentException - If n < 0.

ApfloatRuntimeException

Since:

1.14.0

bernoulliB

public Apcomplex bernoulliB(long n,
                            Apcomplex z)
                     throws java.lang.IllegalArgumentException,
                            ApfloatRuntimeException

Bernoulli polynomial.

Parameters:

n - The first argument.

z - The second argument.

Returns:

B_n(z)

Throws:

java.lang.IllegalArgumentException - If n < 0.

ApfloatRuntimeException

Since:

1.14.0

harmonicNumber

public Apcomplex harmonicNumber(Apcomplex z)
                         throws java.lang.ArithmeticException,
                                ApfloatRuntimeException

Harmonic number.

Parameters:

z - The argument.

Returns:

H_z

Throws:

java.lang.ArithmeticException - If z is a negative integer.

ApfloatRuntimeException

Since:

1.14.0

harmonicNumber

public Apcomplex harmonicNumber(Apcomplex z,
                                Apcomplex r)
                         throws java.lang.ArithmeticException,
                                ApfloatRuntimeException

Generalized harmonic number.

Parameters:

z - The first argument.

r - The second argument.

Returns:

H_z^(r)

Throws:

java.lang.ArithmeticException - If z is a negative integer, unless r has a negative real part or is zero.

ApfloatRuntimeException

Since:

1.14.0

polylog

public Apcomplex polylog(Apcomplex ν,
                         Apcomplex z)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException

Polylogarithm.

Parameters:

\u03bd - The first argument.

z - The second argument.

Returns:

Li_ν(z)

Throws:

java.lang.ArithmeticException - If the real part of ν is ≤ 1 and z is 1.

ApfloatRuntimeException

Since:

1.14.0

logisticSigmoid

public Apcomplex logisticSigmoid(Apcomplex z)
                          throws java.lang.ArithmeticException,
                                 ApfloatRuntimeException

Logistic sigmoid.

Parameters:

z - The argument.

Returns:

σ(z)

Throws:

java.lang.ArithmeticException - If z is an odd integer multiple of π i.

ApfloatRuntimeException

Since:

1.14.0

ulp

public Apfloat ulp(Apcomplex z)
            throws ApfloatRuntimeException

Unit in the last place.

Parameters:

z - The operand.

Returns:

The unit in the last place.

Throws:

ApfloatRuntimeException

Since:

1.10.0

precision

public long precision()

Returns the precision, which is used for the results.

Returns:

The precision of the results.

valueOf

Apfloat valueOf(Apfloat x)
         throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

pi

Apfloat pi()
    throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

pi

Apfloat pi(int radix)
    throws java.lang.NumberFormatException,
           ApfloatRuntimeException

Throws:

java.lang.NumberFormatException

ApfloatRuntimeException

setTrigonometricPrecision

Apfloat setTrigonometricPrecision(Apfloat x)
                           throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

setExponentialPrecision

Apfloat setExponentialPrecision(Apfloat x)
                         throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

setLogarithmicPrecision

Apfloat setLogarithmicPrecision(Apfloat x)
                         throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

setGammaPrecision

Apfloat setGammaPrecision(Apfloat x)

setZetaPrecision

Apfloat setZetaPrecision(Apfloat x)

setErfPrecision

Apfloat setErfPrecision(Apfloat x)

setPrecision

private Apcomplex setPrecision(Apcomplex z)
                        throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

setPrecision

private Apcomplex[] setPrecision(Apcomplex[] z)
                          throws ApfloatRuntimeException

Throws:

ApfloatRuntimeException

setExpTrigPrecision

private Apcomplex setExpTrigPrecision(Apcomplex z)

setTrigExpPrecision

private Apcomplex setTrigExpPrecision(Apcomplex z)

setLogarithmicPrecision

private Apcomplex setLogarithmicPrecision(Apcomplex z)

setGammaPrecision

private Apcomplex setGammaPrecision(Apcomplex z)

setZetaPrecision

private Apcomplex setZetaPrecision(Apcomplex z)

setErfPrecision

private Apcomplex setErfPrecision(Apcomplex z)

checkSmallLinear

private Apcomplex checkSmallLinear(Apcomplex z)