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Summing one- and two-dimensional series related to the Euler series. (English) Zbl 1002.11021

The authors compute double series appearing in Feynman diagram calculations. A typical example is

n=1 + j=1 kn 1 n 2 j=k 2 2 + 3 2kζ(3)+π j=1 k-1 jCl 2 2πj k,

where the Clausen function Cl 2 is defined by Cl 2 (θ)= p=1 + sinpθ p 2 .

11B83Special sequences of integers and polynomials
33E20Functions defined by series and integrals
81T18Feynman diagrams
40A30Convergence and divergence of series and sequences of functions