Some infinite series related to Feynman diagrams

Details Some infinite series related to Feynman diagrams Some infinite series related to Feynman diagrams

2000-10-20

arxiv.org/abs/math-ph/0010026v1

J.Comput.Appl.Math. 140 (2002) 659-671

Physics

Mathematical Physics

10 pages, LaTeX, 2 figures; presented at ICCAM-2000

Scientific paper

Results are presented for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-, two- and three-dimensional series. The sums of these series can be evaluated with the help of various integral representations for hypergeometric functions, and expressed in terms of $\zeta(2)$, $\zeta(3)$, the Catalan constant $G$ and ${\rm Cl}_2(\pi/3)$ where ${\rm Cl}_2(\theta)$ is Clausen's function.

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