Arbitrary-precision computation of the gamma function

09/17/2021
by   Fredrik Johansson, et al.
0

We discuss the best methods available for computing the gamma function Γ(z) in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small arguments; low or high precision; with or without precomputation. The methods also cover the log-gamma function logΓ(z), the digamma function ψ(z), and derivatives Γ^(n)(z) and ψ^(n)(z). Besides attempting to summarize the existing state of the art, we present some new formulas, estimates, bounds and algorithmic improvements and discuss implementation results.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/22/2018

Numerical integration in arbitrary-precision ball arithmetic

We present an implementation of arbitrary-precision numerical integratio...
research
02/12/2023

Numerical methods and arbitrary-precision computation of the Lerch transcendent

We examine the use of the Euler-Maclaurin formula and new derived unifor...
research
06/22/2016

Computing hypergeometric functions rigorously

We present an efficient implementation of hypergeometric functions in ar...
research
05/09/2017

Computing the Lambert W function in arbitrary-precision complex interval arithmetic

We describe an algorithm to evaluate all the complex branches of the Lam...
research
07/03/2021

A fast algorithm for computing the Boys function

We present a new fast algorithm for computing the Boys function using no...
research
06/07/2022

On Binomial coefficients of real arguments

As is well-known, a generalization of the classical concept of the facto...
research
11/22/2020

Fresnel Integral Computation Techniques

This work is an extension of previous work by Alazah et al. [M. Alazah, ...

Please sign up or login with your details

Forgot password? Click here to reset