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.
NumExp: Numerical epsilon expansion of hypergeometric functions
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abstract
It is demonstrated that the well-regularized hypergeometric functions can be evaluated directly and numerically. The package NumExp is presented for expanding hypergeometric functions and/or other transcendental functions in a small regularization parameter. The hypergeometric function is expressed as a Laurent series in the regularization parameter and the coefficients are evaluated numerically by using the multi-precision finite difference method. This elaborate expansion method works for a wide variety of hypergeometric functions, which are needed in the context of dimensional regularization for loop integrals. The divergent and finite parts can be extracted from the final result easily and simultaneously. In addition, there is almost no restriction on the parameters of hypergeometric functions.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
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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.