This module provides implementation for various special functions
Most of them provide besides the regular call raw and fast options clls that are speedier but with possible limitations on corner cases response, valid range and accuracy, raw always being the most dirty.
These version are to be used with caution.
Required header:
Variables | |
| constexpr auto | eve::beta = functor<beta_t> |
| elementwise_callable object computing the beta function: \(\displaystyle \mathbf{B}(x, y) = \frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}\). | |
| constexpr auto | eve::betainc = functor<betainc_t> |
| Computes the betainc incomplete function. \(\displaystyle \mbox{I}_s(x,y) =
\frac{1}{\mbox{B}(x,y)}\int_0^s t^{x-1}(1-t)^{y-1}\mbox{d}t\). | |
| constexpr auto | eve::betainc_inv = functor<betainc_inv_t> |
| elementwise_callable object computing the inverse relative to the first parameter of the beta incomplete function. | |
| constexpr auto | eve::cos_int = functor<cos_int_t> |
| elementwise_callable object computing the cosine integral \( \mathbf{Ci}(x) = \displaystyle -\int_x^\infty \frac{\cos t}{t}\;\mbox{d}t\). | |
| constexpr auto | eve::dawson = functor<dawson_t> |
| elementwise_callable object computing the Dawson function: \(\displaystyle D_+(x)=e^{-x^2}\int_0^{x} e^{t^2} \mbox{d}t\) | |
| constexpr auto | eve::digamma = functor<digamma_t> |
| elementwise_callable object computing the Digamma function i.e. the logarithmic derivative of the \(\Gamma\) function. | |
| constexpr auto | eve::erf = functor<erf_t> |
| elementwise_callable object computing the error function: \( \displaystyle
\mbox{erf}(x)=\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\). | |
| constexpr auto | eve::erf_inv = functor<erf_inv_t> |
| elementwise_callable object computing the inverse of the error function. | |
| constexpr auto | eve::erfc = functor<erfc_t> |
| elementwise_callable object computing the complementary error function \( \displaystyle
\mbox{erf}(x)=1-\frac{2}{\sqrt\pi}\int_0^{x} e^{-t^2}\mbox{d}t\) | |
| constexpr auto | eve::erfc_inv = functor<erfc_inv_t> |
| Computes the inverse of the complementary error function. | |
| constexpr auto | eve::erfcx = functor<erfcx_t> |
| Computes the normalized complementary error function \( \displaystyle \mbox{erfcx}(x) = e^{x^2} \mbox{erfc}(x)\). | |
| constexpr auto | eve::exp_int = functor<exp_int_t> |
| elementwise_callable object computing the exponential integral \( \mathbf{E}_n(x) = \displaystyle \int_1^\infty \frac{e^{-xt}}{t^n}\;\mbox{d}t\). | |
| constexpr auto | eve::factorial = functor<factorial_t> |
| elementwise_callable computing \(\displaystyle n! = \prod_{i=1}^n i\). | |
| constexpr auto | eve::gamma_p = functor<gamma_p_t> |
| elementwise_callable object computing the normalized lower incomplete \(\Gamma\) function. | |
| constexpr auto | eve::gamma_p_inv = functor<gamma_p_inv_t> |
| elementwise_callable object computing the inverse of the normalized lower incomplete \(\Gamma\) function. | |
| constexpr auto | eve::hurwitz = functor<hurwitz_t> |
| elementwise_callable object computing the Hurwitz function i.e. \(\sum_{k=0}^\infty (k+z)^{-s}\), where any term with \(k+z = 0\) is excluded. | |
| constexpr auto | eve::lambert = functor<lambert_t> |
| Computes the inverse of the function \( x \rightarrow xe^x \). | |
| constexpr auto | eve::lbeta = functor<lbeta_t> |
| elementwise_callable object computing the natural logarithm of the beta function. | |
| constexpr auto | eve::lfactorial = functor<lfactorial_t> |
| elementwise_callable object computing the natural logarithm of the factorial of unsigned integer values \(\displaystyle \log n! = \sum_{i=1}^n \log i\). | |
| constexpr auto | eve::log_abs_gamma = functor<log_abs_gamma_t> |
| elementwise_callable object computing the natural logarithm of the absolute value of the \(\Gamma\) function. | |
| constexpr auto | eve::log_gamma = functor<log_gamma_t> |
| elementwise_callable object computing the natural logarithm of the \(\Gamma\) function. | |
| constexpr auto | eve::lrising_factorial = functor<lrising_factorial_t> |
| elementwise_callable object computing the natural logarithm of the rising Factorial function i.e. \(\log\left(\frac{\Gamma(x+a)}{\Gamma(x)}\right)\). | |
| constexpr auto | eve::omega = functor<omega_t> |
| Computes the Wright \(\omega\) the inverse function of \( x \rightarrow \log
x+x\). | |
| constexpr auto | eve::polygamma = functor<polygamma_t> |
| elementwise_callable object computing the Polygamma function i.e. the nth derivative of the digamma function | |
| constexpr auto | eve::rising_factorial = functor<rising_factorial_t> |
| elementwise_callable object computing the rising Factorial function i.e. \(\frac{\Gamma(x+a)}{\Gamma(x)}\). | |
| constexpr auto | eve::signgam = functor<signgam_t> |
| elementwise_callable object computing the sign of the \(\Gamma\) function. | |
| constexpr auto | eve::sin_int = functor<sin_int_t> |
| elementwise_callable object computing the sine integral \( \mathbf{Si}(x) = \displaystyle \int_0^x \frac{\sin t}{t}\;\mbox{d}t\). | |
| constexpr auto | eve::stirling = functor<stirling_t> |
| elementwise_callable object computing the Stirling approximation of the \(\Gamma\) function. | |
| constexpr auto | eve::tgamma = functor<tgamma_t> |
| elementwise_callable object computing \(\displaystyle \Gamma(x)=\int_0^\infty t^{x-1}e^{-t}\mbox{d}t\). | |
| constexpr auto | eve::trigamma = functor<trigamma_t> |
| elementwise_callable object computing the Trigamma function i.e. the second derivative of the \(\log\Gamma\) function. | |
| constexpr auto | eve::zeta = functor<zeta_t> |
| Computes the Riemann \(\zeta\) function. | |
