- XSummer - Transcendental Functions and Symbolic Summation in Form

Abstract

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their generalizations appear as building blocks, originating for example from the expansion of generalized hypergeometric functions around integer values of the parameters. In this Letter we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.

21 pages, 1 figure, Latex

References in corpus (12)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Harmonic Polylogarithms
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Harmonic sums, Mellin transforms and Integrals
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• Algebraic Relations Between Harmonic Sums and Associated Quantities
• Expansion around half-integer values, binomial sums and inverse binomial sums
• Symbolic Expansion of Transcendental Functions
• Scalar One-Loop Integrals using the Negative-Dimension Approach
• Application of the negative-dimension approach to massless scalar box integrals
• Two-loop amplitudes with nested sums: Fermionic contributions to e+ e- --> q qbar g
• Tuning FORM with large calculations

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