Elliptic functions

Detailed Description

This module provides implementation for scalar and SIMD versions of elliptic functions.

Convenience header:

#include <eve/module/elliptic.hpp> 

Variables
constexpr auto	eve::ellint_1 = functor<ellint_1_t>
	elementwise_callable object computing the elliptic integrals of the first kind.
constexpr auto	eve::ellint_2 = functor<ellint_2_t>
	elementwise_callable object computing the elliptic integrals of the second kind.
constexpr auto	eve::ellint_d = functor<ellint_d_t>
	elementwise_callable object computing the \(\mbox{D}\) elliptic integral.
constexpr auto	eve::ellint_rc = functor<ellint_rc_t>
	elementwise_callable object computing the degenerate Carlson's elliptic integral \( \mathbf{R}_\mathbf{C}(x, y) = \frac12 \int_{0}^{\infty} \scriptstyle(t+x)^{-1/2}(t+y)^{-1}\scriptstyle\;\mathrm{d}t\).
constexpr auto	eve::ellint_rd = functor<ellint_rd_t>
	elementwise_callable object computing the Carlson's elliptic integral \( \mathbf{R}_\mathbf{D}(x, y) = \frac32 \int_{0}^{\infty} \scriptstyle[(t+x)(t+y)]^{-1/2} (t+z)^{-3/2}\scriptstyle\;\mathrm{d}t\).
constexpr auto	eve::ellint_rf = functor<ellint_rf_t>
	Computes the Carlson's elliptic integral \( \mathbf{R}_\mathbf{F}(x, y) = \frac32 \int_{0}^{\infty} \scriptstyle[(t+x)(t+y)]^{-1/2} (t+z)^{-3/2}\scriptstyle\;\mathrm{d}t\).
constexpr auto	eve::ellint_rg = functor<ellint_rg_t>
	Computes the Carlson's elliptic integral \( \mathbf{R}_\mathbf{G}(x, y) = \frac1{4\pi} \int_{0}^{2\pi}\int_{0}^{\pi} \scriptstyle\sqrt{x\sin^2\theta\cos^2\phi +y\sin^2\theta\sin^2\phi +z\cos^2\theta} \scriptstyle\;\mathrm{d}\theta\;\mathrm{d}\phi\).
constexpr auto	eve::ellint_rj = functor<ellint_rj_t>
	Computes the Carlson's elliptic integral \( \mathbf{R}_\mathbf{J}(x, y) = \frac32 \int_{0}^{\infty} \scriptstyle(t+p)^{-1}[(t+x)(t+y)(t+z)]^{-1/2}\scriptstyle\;\mathrm{d}t\).