6533b860fe1ef96bd12c3818
RESEARCH PRODUCT
Fourier series for elliptic integrals and some generalizations via hypergeometric series
John T. Conwaysubject
Carlson symmetric formBasic hypergeometric seriesPure mathematicsLegendre formAppell seriesBilateral hypergeometric seriesApplied MathematicsMathematical analysisConjugate Fourier seriesGeneralized hypergeometric functionFourier seriesAnalysisMathematicsdescription
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, and the Fourier coefficients are given in terms of the Kampe de Feriet function for all cases.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-05-01 | Integral Transforms and Special Functions |