Series and epsilon-expansion of the hypergeometric functions

Abstract

Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.

5 pages, to appear in the proceedings of 7th DESY Workshop on Elementary Particle Theory "Loops and Legs in Quantum Field Theory", April 25 -30, 2004, Zinnowitz (Usedom Island), Germany

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• Non-abelian expansion of S-matrix elements and non-abelian tachyon DBI action
• When epsilon-expansion of hypergeometric functions is expressible in terms of multiple polylogarithms: the two-variables examples
• Expansion of hypergeometric functions in terms of polylogarithms with nontrivial variable change