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

Authors:
Mark W. Coffey
Affiliations:
Department of Physics, Colorado School of Mines, 16th and Illinois Sts., Golden, CO 80401, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

We consider summations over digamma and polygamma functions, often with summands of the form (+/-1)^n@j(n+p/q)/n^r and (+/-1)^n@j^(^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.