Search results for "Bilateral hypergeometric series"

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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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Fourier series for elliptic integrals and some generalizations via hypergeometric series

2008

Fourier series are derived for generalizations of the three canonical Legendre incomplete elliptic integrals using a hypergeometric series approach. The Fourier series for the incomplete Epstein–Hubbell integrals are obtained as special cases of the generalization of the Legendre integrals of the first and second kinds. The Fourier series for the integrals of the first and second kinds, and those for the Epstein–Hubbell integrals, were obtained recently using a different approach, but the series obtained for the generalization of the incomplete integral of the third kind is new. All cases of the integral of the third kind are given, with the modulus and the parameter being complex variables…

Carlson symmetric formBasic hypergeometric seriesPure mathematicsLegendre formAppell seriesBilateral hypergeometric seriesApplied MathematicsMathematical analysisConjugate Fourier seriesGeneralized hypergeometric functionFourier seriesAnalysisMathematicsIntegral Transforms and Special Functions
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