Summing one- and two-dimensional series related to the Euler series

TL;DR

This paper analyzes infinite series related to the Euler series, especially those appearing in Feynman diagram calculations, expressing many in terms of special constants like zeta values and Clausen's function.

Contribution

It provides new results for summing one- and two-dimensional series connected to the Euler series, with explicit expressions involving special mathematical constants.

Findings

Series expressed in terms of zeta(2), zeta(3), G, and Cl2(pi/3)

Results applicable to Feynman diagram calculations

Enhanced understanding of series related to Euler series

Abstract

We present results for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-dimensional and two-dimensional series. Most of these series can be expressed in terms of zeta(2), zeta(3), the Catalan constant G and Cl{2}(pi/3) where Cl{2}(theta) is Clausen's function.