E.V.E  0.1-beta

Detailed Description

These functions provide scalar and SIMD version of special functions.

Convenience header:

#include <eve/function/special.hpp>

Variables

constexpr callable_beta_ eve::beta = {}
 Callable object computing the beta function. \(\mbox{B}(x,y)=\int_0^1 t^{x-1}(1-t)^{y-1}\mbox{d}t\). More...
 
constexpr callable_betainc_ eve::betainc = {}
 Callable object computing the beta incomplete function. \(\mbox{B}(s,x,y)=\frac{1}{\mbox{B}(x,y)}\int_0^s t^{x-1}(1-t)^{y-1}\mbox{d}t\). More...
 
constexpr callable_betainc_inv_ eve::betainc_inv = {}
 Callable object computing the inverse relative to the first parameter of the beta incomplete function. More...
 
constexpr callable_dawson_ eve::dawson = {}
 Callable object computing the dawson function. \(\displaystyle D_+(x)=e^{-x^2}\int_0^{x} e^{t^2} \mbox{d}t\). More...
 
constexpr callable_digamma_ eve::digamma = {}
 Callable object computing logarithmic derivative of the \(\Gamma\) function. More...
 
constexpr callable_erf_ eve::erf = {}
 Callable object computing the eroror function. \( \mbox{erf}(x)=\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\). More...
 
constexpr callable_erf_inv_ eve::erf_inv = {}
 Callable object computing the inverse of the \(\mbox{erf}\) function. More...
 
constexpr callable_erfc_ eve::erfc = {}
 Callable object computing the complementary error function \(1-\mbox{erf}(x)\). More...
 
constexpr callable_erfc_inv_ eve::erfc_inv = {}
 Callable object computing the inverse of the \(\mbox{erfc}\) function. More...
 
constexpr callable_erfcx_ eve::erfcx = {}
 Callable object computing the normalized complementary error function \(\mbox{erfcx}(x) = e^{x^2} \mbox{erfc}(x)\). More...
 
constexpr callable_exp_int_ eve::exp_int = {}
 Callable object computing the exponential integral \(\displaystyle \mbox{E}_{n}(x)=\int_0^\infty \frac{e^{-xt}}{t^{n}} \mbox{d}t\). More...
 
constexpr callable_gamma_p_ eve::gamma_p = {}
 Callable object computing the normalized lower incomplete \(\Gamma\) function : \(\displaystyle \frac{1}{\Gamma(x)}\int_0^{y} t^{x-1}e^{-t}\mbox{d}t\). More...
 
constexpr callable_gamma_p_inv_ eve::gamma_p_inv = {}
 Callable object computing the normalized lower incomplete \(\Gamma\) function. More...
 
constexpr callable_lbeta_ eve::lbeta = {}
 Callable object computing the logarithm of the beta function. More...
 
constexpr callable_lgamma_ eve::lgamma = {}
 Callable object computing the logarithm of the \(\Gamma\) function. More...
 
constexpr callable_signgam_ eve::signgam = {}
 Callable object computing the sign of the \(\Gamma\) function. More...
 
constexpr callable_stirling_ eve::stirling = {}
 Callable object computing an approximation of the \(\Gamma\) function by \(\displaystyle \Gamma(x) \approx \sqrt{2 \pi} x^{x-\frac12} e^{-x} \left( 1 + \frac1{x} P(\frac1{x})\right)\), where \(P\) is a polynomial. More...
 
constexpr callable_tgamma_ eve::tgamma = {}
 Callable object computing the (true) \(\Gamma\) function: \(\displaystyle \Gamma(x)=\int_0^\infty t^{x-1}e^{-t}\mbox{d}t\). More...
 
constexpr callable_zeta_ eve::zeta = {}
 Callable object computing the the Riemann \(\zeta\) function: \(\displaystyle \zeta(s)=\sum_{n=0}^\infty \frac1{n^s}\). More...