On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:183

Article

Coffey, MW

关键词: gamma function;    digamma function;    polygamma function;    Riemann zeta function;    Clausen function;    Euler sums;    harmonic numbers;    Hurwitz zeta function;    hypergeometric function;    dilogarithm function;    trilogarithm function;    polylogarithm function;   

DOI  :  10.1016/j.cam.2005.01.003

来源: Elsevier

【 摘 要 】

We consider summations over digamma and polygamma functions, often with summands of the form (+/- 1)(n)psi(n + p/q) n(r) and (+/- 1)psi((m)) (n +p/q)/n(r), where m, p, q, and r are positive integers. We develop novel general integral representations and present explicit examples. Special cases of the sums reduce to known linear Euler sums. The sums of interest find application in quantum field theory, including evaluation of Feynman amplitudes. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free