E.V.E
v2023.02.15
Special functions

Detailed Description

Special functions.

This module provides implementation for various special functions

Required header:

#include <eve/module/special.hpp>

Variables

constexpr callable_deta_ eve::deta = {}
 Callable object computing \( \displaystyle \sum_0^\infty \frac{(-1)^n}{(kn+1)^z}\). More...
 
constexpr callable_eta_ eve::eta = {}
 Callable object computing The imaginary error function \( \displaystyle \mathrm{erfi}(z) = -i/erf(iz)\). More...
 
constexpr callable_faddeeva_ eve::faddeeva = {}
 Callable object computing \(e^{-z^2}\mathrm{erfc}(-iz)\) the scaled complex error func. More...
 
constexpr callable_lambda_ eve::lambda = {}
 Callable object computing The Dirichlet \( \displaystyle \lambda(z) = \sum_0^\infty \frac{1}{(2n+1)^z}\). More...
 
constexpr callable_beta_ eve::beta = {}
 Computes the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\) is returned. More...
 
constexpr callable_betainc_ eve::betainc = {}
 Computes the beta incomplete function. \(\displaystyle \mbox{I}_s(x,y) = \frac{1}{\mbox{B}(x,y)}\int_0^s t^{x-1}(1-t)^{y-1}\mbox{d}t\). More...
 
constexpr callable_betainc_inv_ eve::betainc_inv = {}
 Computes the inverse relative to the first parameter of the beta incomplete function. More...
 
constexpr callable_dawson_ eve::dawson = {}
 Computes the Dawson function \(\displaystyle D_+(x)=e^{-x^2}\int_0^{x} e^{t^2} \mbox{d}t\). More...
 
constexpr callable_digamma_ eve::digamma = {}
 Computes the Digamma function i.e. the logarithmic derivative of the \(\Gamma\) function. More...
 
constexpr callable_double_factorial_ eve::double_factorial = {}
 Computes the double factorial of n More...
 
constexpr callable_erf_ eve::erf = {}
 Computes the error function: \( \displaystyle \mbox{erf}(x)=\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\) or its analytic continuation in the complex plane. More...
 
constexpr callable_erf_inv_ eve::erf_inv = {}
 Computes the inverse of the error function. More...
 
constexpr callable_erfc_ eve::erfc = {}
 Computes the complementar error function \( \displaystyle \mbox{erf}(x)=1-\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\). More...
 
constexpr callable_erfc_inv_ eve::erfc_inv = {}
 Computes the complementar error function \( \displaystyle \mbox{erf}(x)=1-\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\). More...
 
constexpr callable_erfcx_ eve::erfcx = {}
 Computes the normalized complementary error function \( \displaystyle \mbox{erfcx}(x) = e^{x^2} \mbox{erfc}(x)\). More...
 
constexpr callable_exp_int_ eve::exp_int = {}
 Computes the exponential integral \( \mathbf{E}_n(x) = \displaystyle \int_1^\infty \frac{e^{-xt}}{t^n}\;\mbox{d}t\). More...
 
constexpr callable_factorial_ eve::factorial = {}
 Computes \(\displaystyle n! = \prod_{i=1}^n i\). More...
 
constexpr callable_gamma_p_ eve::gamma_p = {}
 Computes the normalized lower incomplete \(\Gamma\) function. More...
 
constexpr callable_gamma_p_inv_ eve::gamma_p_inv = {}
 Computes the inverse of the normalized lower incomplete \(\Gamma\) function. More...
 
constexpr callable_lambert_ eve::lambert = {}
 Computes the inverse of the function \( x \rightarrow xe^x \). More...
 
constexpr callable_lbeta_ eve::lbeta = {}
 Computes the natural logarithm of the beta function. More...
 
constexpr callable_lfactorial_ eve::lfactorial = {}
 Computes the natural logarithm of the factorial of unsigned integer values \(\displaystyle \log n! = \sum_{i=1}^n \log i\). More...
 
constexpr callable_log_abs_gamma_ eve::log_abs_gamma = {}
 Computes the natural logarithm of the absolute value of the \(\Gamma\) function. More...
 
constexpr callable_log_gamma_ eve::log_gamma = {}
 Computes the natural logarithm of the \(\Gamma\) function. More...
 
constexpr callable_lrising_factorial_ eve::lrising_factorial = {}
 Computes the natural logarithm of the Rising Factorial function i.e. \(\log\left(\frac{\Gamma(x+a)}{\Gamma(x)}\right)\). More...
 
constexpr callable_omega_ eve::omega = {}
 Computes the the Wright \(\omega\) the inverse function of \( x \rightarrow \log x+x\). More...
 
constexpr callable_rising_factorial_ eve::rising_factorial = {}
 Computes the Rising Factorial function i.e. \(\frac{\Gamma(x+a)}{\Gamma(x)}\). More...
 
constexpr callable_signgam_ eve::signgam = {}
 Computes the sign of the \(\Gamma\) function. More...
 
constexpr callable_stirling_ eve::stirling = {}
 Computes the Stirling approximation of the \(\Gamma\) function. More...
 
constexpr callable_tgamma_ eve::tgamma = {}
 Computes \(\displaystyle \Gamma(x)=\int_0^\infty t^{x-1}e^{-t}\mbox{d}t\) or its analytic continuation in the complex plane. More...
 
constexpr callable_zeta_ eve::zeta = {}
 Computes the Riemann \(\zeta\) function. More...