Special functions (vp.special)

Special functions that physics codes evaluate in their inner loops.

• the Boys function of Gaussian integrals
• the plasma dispersion function
• the Faddeeva function

Part of the distribution vipyr; it runs from a checkout of the repository. Planned on PyPI as pip install vipyr.

Functions

vp.special.boys

The Boys functions F_0(T) .. F_nmax(T), as an array of nmax + 1 values, with F_n(T) = int_0^1 t^(2n) exp(-T t^2) dt. Orders 0 to 16, T >= 0.

vp.special.faddeeva_w

The Faddeeva function w(z) = exp(-z^2) erfc(-i z).

vp.special.plasma_z

The plasma dispersion function Z(zeta) = i sqrt(pi) w(zeta) and its derivative Z'(zeta) = -2 (1 + zeta Z(zeta)), anywhere in the plane.

Examples in the gallery

• The Boys function, the integral behind Gaussian basis sets
• Landau damping at four wavelengths
• The Faddeeva and plasma dispersion functions on the complex plane