Special functions.
This module provides implementation for various special functions
Required header:
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 Dirichlet \( \displaystyle \eta(z) = \sum_0^\infty \frac{(-1)^n}{(n+1)^z}\). 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... | |