On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams
| Autor: | Mark W. Coffey |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
FOS: Physical sciences
Trilogarithm function Clausen function Hurwitz zeta function symbols.namesake Harmonic numbers Feynman diagram Riemann zeta function Hypergeometric function Gamma function Mathematical Physics Mathematics Discrete mathematics Applied Mathematics Mathematical Physics (math-ph) Polygamma function Euler sums Dilogarithm function Algebra Computational Mathematics Digamma function symbols Polylogarithm function |
| Zdroj: | Journal of Computational and Applied Mathematics. 183:84-100 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2005.01.003 |
| Popis: | We consider summations over digamma and polygamma functions, often with summands of the form (\pm 1)^n\psi(n+p/q)/n^r and (\pm 1)^n\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. Comment: to appear in J. Comput. Appl. Math.; corrected proof available online with this journal; no figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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