On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams
作者：
Highlights：
•
摘要
We consider summations over digamma and polygamma functions, often with summands of the form (±1)nψ(n+p/q)/nr and (±1)nψ(m)(n+p/q)/nr, 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.
论文关键词：33B,33E,11M,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
论文评审过程：Received 5 November 2004, Revised 3 January 2005, Available online 2 March 2005.
论文官网地址：https://doi.org/10.1016/j.cam.2005.01.003
