Φ(x) = ϕ(r), r = ∥x∥_{2}  f(r) = φ(ω), r = ∥ω∥_{2}  G(h)

r^{β}, β ∈ IR_{>0} \ 2IN  2^{d+β}π^{d/2} \frac{Γ(\frac{d + β}{2} )}{Γ(−\frac{β}{2} )} r^{−d−β}

thin–plate splines  \frac{Γ (\frac{d + β}{2} )}{Γ (−\frac{β}{2} ) Γ (\frac{d}{2} + 1)} · \frac{h^{β}}{2^{2d+1}(6.38d)^{β}}

(−1)^{1+β/2}r^{β} log r, β ∈ 2IN 2^{d+β−1}π^{d/2}Γ (\frac{d + β}{2} ) β!r^{−d−β}

thin–plate splines  \frac{Γ (\frac{d + β}{2} )}{Γ (\frac{d}{2} + 1)} · \frac{β!h^{β}}{2^{2d+2}(6.38d)^{β}}

(γ^{2} + r^{2})^{β/2}, β ∈ IR \ 2IN_{≥0}  \frac{2π^{d/2}}{Γ(−\frac{β}{2} )} K_{ν}(γr) (\frac{r}{2γ} )^{−ν}  c_{1}(β, d)h^{β} exp (−2γ \frac{6.38d}{h} ),

c_{1}(β, d) := \frac{Γ (\frac{d + β}{2} )}{Γ (−\frac{β}{2} ) Γ (\frac{d}{2} + 1) 2^{2d+1}(6.38d)^{β}}

e^{−βr^{2}}, β > 0  (\frac{π}{β} )^{d/2} e^{−r^{2}/4β}  \frac{1}{2^{2d+1}Γ (\frac{d}{2} + 1)} (\frac{6.38d}{h\sqrt{β}} )^{d} exp (− (\frac{6.38d}{h\sqrt{β}} )^{2})

\frac{2π^{d/2}}{Γ(k)} K_{k−d/2}(r)(r/2)^{k−d/2}  (1 + r^{2})^{−k}  \frac{h^{2k−d}}{2^{2k+2d+1}π^{d/2}Γ (\frac{d}{2} + 1)} · \frac{1}{(6.38d)^{2k−d}} · (1 + \frac{h^{2}}{162.8d^{2}} )^{−k}

Table 2: These table entries explicitly contain the relevant constants, though not in optimal form.