Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals

Details Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals

2001-10-05

arxiv.org/abs/hep-ph/0110083v2

J.Math.Phys. 43 (2002) 3363-3386

Physics

High Energy Physics

High Energy Physics - Phenomenology

28 pages, minor changes

Scientific paper

Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools are based on nested sums and can be formulated as algorithms suitable for an implementation on a computer. Examples, such as expansions of generalized hypergeometric functions or Appell functions are discussed. As a further application, we give the general solution of a two-loop integral, the so-called C-topology, in terms of multiple nested sums. In addition, we discuss some important properties of nested sums, in particular we show that they satisfy a Hopf algebra.

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