Search results for "Appell function"

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Simple connections between generalized hypergeometric series and dilogarithms

1997

AbstractConnections between generalized hypergeometric series and dilogarithms are investigated. Some simple relations of an Appell's function and dilogarithms are found.

Appell functionDilogarithmBasic hypergeometric seriesConfluent hypergeometric functionAppell seriesBilateral hypergeometric seriesApplied MathematicsMathematics::Classical Analysis and ODEsGeneralized hypergeometric functionMathematics::Geometric TopologyHypergeometric seriesAlgebraHigh Energy Physics::TheoryComputational MathematicsHypergeometric identityMathematics::K-Theory and HomologyMathematics::Quantum AlgebraLauricella hypergeometric seriesHypergeometric functionMathematicsJournal of Computational and Applied Mathematics
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Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams

2000

Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams. Currently, large effort is devoted to the search for closed expressions of loop integrals, written whenever possible in terms of known - often hypergeometric-type - functions. In this work, the scalar three-point function is re-evaluated by means of generalized hypergeometric functions of two variables. Finally, use is made of the connection between such Appell functions and dilogarithms coming from a previous investigation, to recover well-known results.

Appell functionLoop integralDilogarithmAppell seriesApplied MathematicsScalar (mathematics)Feynman diagramFOS: Physical sciencesFísicaMathematical Physics (math-ph)Generalized hypergeometric functionLoop integralHypergeometric seriesAlgebraIntegral calculussymbols.namesakeComputational MathematicsHigh Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)symbolsFeynman diagramHypergeometric functionMathematical PhysicsPochhammer symbolMathematics
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