Some infinite series related to Feynman diagrams

DOI10.1016/S0377-0427(01)00487-3zbMath0993.81039arXivmath-ph/0010026MaRDI QIDQ1602806

Per Osland, Odd Magne Ogreid

Publication date: 24 June 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0010026

zbMATH Keywords

Riemann zeta functionpolylogarithmsEuler seriesCatalan constantClausen's functionintegral representations for hypergeometric functions

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Feynman diagrams (81T18) Computational methods for problems pertaining to quantum theory (81-08) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Other functions defined by series and integrals (33E20) Generalized hypergeometric series, ({}_pF_q) (33C20) Approximation to limiting values (summation of series, etc.) (40A25) Multiple sequences and series (40B05) Zeta and (L)-functions: analytic theory (11M99)

Related Items (5)

Monotonic properties for ratio of the generalized (p,k)-polygamma functions ⋮ Scaling, renormalization and statistical conservation laws in the Kraichnan model of turbulent advection ⋮ Series representations for the Apéry constant \(\zeta (3)\) involving the values \(\zeta (2n)\) ⋮ Monotonicity, concavity, and inequalities related to the generalized digamma function ⋮ On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams

Cites Work

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• On Nielsen's generalized polylogarithms and their numerical calculation
• Single-scale diagrams and multiple binomial sums
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• More series related to the Euler series.

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