Detailed Description
These functions provide scalar and SIMD version of some elliptic functions.
Convenience header:
#include <eve/function/elliptic.hpp>
Variables | |
constexpr callable_ellint_1_ | eve::ellint_1 = {} |
Callable object computing the elliptic integrals of the first kind : \(\int_0^{\phi} \frac{\mathrm{d}t}{\sqrt{1-k^2\sin^2 t}}\). More... | |
constexpr callable_ellint_2_ | eve::ellint_2 = {} |
Callable object computing the elliptic integrals of the second kind : \( \int_0^{\phi} \scriptstyle \sqrt{1-k^2\sin^2 t} \scriptstyle\;\mathrm{d}t\). More... | |
constexpr callable_ellint_d_ | eve::ellint_d = {} |
Callable object computing the \(\mbox{D}\) elliptic integrals : \(\int_0^{\phi} \frac{\sin^2 t}{\sqrt{1-k^2\sin^2 t}} \scriptstyle\;\mathrm{d}t\). More... | |
constexpr callable_ellint_rc_ | eve::ellint_rc = {} |
Callable object computing the degenerate Carlson's elliptic integral \( \frac12 \int_{0}^{\infty} \scriptstyle(t+x)^{-1/2}(t+y)^{-1}\scriptstyle\;\mathrm{d}t\). More... | |
constexpr callable_ellint_rd_ | eve::ellint_rd = {} |
Callable object computing the the Carlson's elliptic integral \( \frac32 \int_{0}^{\infty} \scriptstyle[(t+x)(t+y)]^{-1/2} (t+z)^{-3/2}\scriptstyle\;\mathrm{d}t\). More... | |
constexpr callable_ellint_rf_ | eve::ellint_rf = {} |
Callable object computing the Carlson's elliptic integral \(\frac12 \int_{0}^{\infty} \scriptstyle[(t+x)(t+y)(t+z)]^{-1/2}\scriptstyle\;\mathrm{d}t\). More... | |
constexpr callable_ellint_rg_ | eve::ellint_rg = {} |
Callable object computing the the Carlson's elliptic integral \(\frac1{4\pi} \int_{0}^{2\pi}\int_{0}^{\pi} \scriptstyle\sqrt{x\sin^2\theta\cos^2\phi +y\sin^2\theta\sin^2\phi +z\cos^2\theta} \scriptstyle\;\mathrm{d}\theta\;\mathrm{d}\phi\). More... | |
constexpr callable_ellint_rj_ | eve::ellint_rj = {} |
Callable object computing the the Carlson's elliptic integral \(\frac32 \int_{0}^{\infty}\scriptstyle(t+p)^{-1}[(t+x)(t+y)(t+z)]^{-1/2}\scriptstyle\;\mathrm{d}t\). More... | |