Nested sums, expansion of transcendental functions, and multiscale multiloop integrals

DOI10.1063/1.1471366zbMATH Open1060.33007arXivhep-ph/0110083OpenAlexW3105951297MaRDI QIDQ4832666

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Publication date: 14 December 2004

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Abstract: 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.

Full work available at URL: https://arxiv.org/abs/hep-ph/0110083

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