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- W2093899607 abstract "We give a closed-form evaluation of Erdélyi-Kober fractional integrals, involving incomplete elliptic integrals of the first kind, F ( φ, k ), and of the second kind, E ( φ, k ), which are integrated either with respect to the modulus or the amplitude. This is made possible by representing F ( φ, k ) and E ( φ, k ) in terms of the Kampé de Fériet double hypergeometric functions. Reduction formulae for these enable us to simplify the solutions for thirteen special cases, including integrals involving complete elliptic integrals. The hypergeometric character of the incomplete integrals is useful for evaluations of other classes of integrals involving F ( φ, k ) and E ( φ, k )." @default.
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- W2093899607 date "1994-03-08" @default.
- W2093899607 modified "2023-09-27" @default.
- W2093899607 title "On the integration of incomplete elliptic integrals" @default.
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- W2093899607 doi "https://doi.org/10.1098/rspa.1994.0036" @default.
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