A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
Three-loop massive tadpoles and polylogarithms through weight six
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abstract
We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylgarithms of arguments $e^{k i \pi/3}$.
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math-ph 1years
2026 1verdicts
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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.