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

2005/05/19 by Mark W. Coffey, Coffey, Mark W. · 2 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0505051

to appear in J. Comput. Appl. Math.; corrected proof available online with this journal; no figures

arxiv created 2005/05/19 · openalex publication_date 2005/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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