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CERTAIN SUMMATION FORMULAS FOR HUMBERT'S DOUBLE HYPERGEOMETRIC SERIES Ψ2 AND Φ2

  • CHOI, JUNESANG (Department of Mathematics Dongguk University) ;
  • RATHIE, ARJUN KUMAR (Department of Mathematics School of Mathematical and Physical Sciences Central University of Kerala, Riverside Transit Campus)
  • Received : 2015.03.13
  • Published : 2015.10.31

Abstract

The main objective of this paper is to establish certain explicit expressions for the Humbert functions ${\Phi}_2$(a, a + i ; c ; x, -x) and ${\Psi}_2$(a ; c, c + i ; x, -x) for i = 0, ${\pm}1$, ${\pm}2$, ..., ${\pm}5$. Several new and known summation formulas for ${\Phi}_2$ and ${\Psi}_2$ are considered as special cases of our main identities.

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Cited by

  1. On new reduction formulas for the Humbert functions Ψ2, Φ2 and Φ3 vol.28, pp.5, 2017, https://doi.org/10.1080/10652469.2017.1297438