Computing the Barnes G-function and the gamma function in the entire complex plane
Kuznetsov, Alexey1
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作者信息
1. York Univ
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Abstract
We present an algorithm for generating approximations for the logarithm of Barnes G- function in the half-plane Re(z) >= 3/2. These approximations involve only elementary functions and are easy to implement. The algorithm is based on a two-point Pade approximation and we use it to provide two approximations to ln(G(z)), accurate to 3 x 10(-16 )and 3 x 10(-31) in the half-plane Re(z) >= 3/2; a reflection formula is then used to compute Barnes G-function in the entire complex plane. A by-product of our algorithm is that it also produces accurate approximations to the gamma function. (C) 2022 Elsevier B.V. All rights reserved.
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Elsevier