alpha

constexpr double alpha(const int n, const double x) noexcept: Evaluates the alpha function [1] for a complex input.

Parameters

const int n

A nonnegative number.

const double x

A real number.

Returns

double

A real number.

The alpha function is defined as follows:

\[\alpha_n(x) = \int_{1}^{\infty} t^{n}e^{-xt}dt\]

Example

int n = 1;
double x = 1;
std::cout << alpha(n, x) << "\n";

Output:

0.735758

References