Package org.apache.commons.numbers.gamma

Class LanczosApproximation

java.lang.Object
org.apache.commons.numbers.gamma.LanczosApproximation
public final class LanczosApproximation extends Object
Lanczos approximation to the Gamma function. It is related to the Gamma function by the following equation \[ \Gamma(x) = \sqrt{2\pi} \, \frac{(g + x + \frac{1}{2})^{x + \frac{1}{2}} \, e^{-(g + x + \frac{1}{2})} \, \mathrm{lanczos}(x)} {x} \] where \( g \) is the Lanczos constant. See equations (1) through (5), and Paul Godfrey's Note on the computation of the convergent Lanczos complex Gamma approximation.

  • Method Details

    • value

      public static double value(double x)
      Computes the Lanczos approximation.
      Parameters:
      x - Argument.
      Returns:
      the Lanczos approximation.

    • g

      public static double g()
      Return the Lanczos constant \( g = \frac{607}{128} \).
      Returns:
      the Lanczos constant.