We define the incomplete gamma function ratio for positive N by \begin{align*}\tag{1}P(N, b, X) &= \int^X_0 t^{N-1}e^{-bt} dt/ \int^\infty_0 t^{N-1}e^{-bt} dt ...

In this paper, we present a very accurate approximation for the gamma function: [Formula: see text] as [Formula: see text], and we prove that the function [Formula: see text] is strictly decreasing ...

\newenvironment{knitrout}{}{} % an empty environment to be redefined in TeX ...

A Python script that defines the gamma function for all complex numbers, as well as some probability functions related to distributions that use the gamma function. I initially used this function as a ...

The first forty-one coefficients of a continued fraction for $\ln \Gamma(z) + z - (z - 1/2) \ln z - \ln \surd \overline {2\pi}$, are given. The computation, based on Wall's algorithm for converting a ...

Abstract: The residue calculus method of investigation of certain waveguide configurations makes use of the asymptotic properties of the gamma function. Usually the range of the variables concerned is ...