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- XSummer - Transcendental Functions and Symbolic Summation in Form
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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.
Forward citations
Cited by 3 Pith papers
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HyperPrecision: A Mathematica package for High-Precision Numerical Evaluation of Multivariate Hypergeometric Functions
HyperPrecision is a new Mathematica package that evaluates general Horn-type multivariate hypergeometric functions and their ε-expansions to high precision by reducing Pfaffian PDE systems to solvable ODEs.
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Numerical analytical continuation of multivariate hypergeometric functions
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
- IBIS: Inverse BInomial sum Solver
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