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http://dx.doi.org/10.4134/CKMS.2015.30.4.439

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)
Publication Information
Communications of the Korean Mathematical Society / v.30, no.4, 2015 , pp. 439-446 More about this Journal
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.
Keywords
gamma function; Pochhammer symbol; hypergeometric function; generalized hypergeometric function; Kummer's second summation theorem; Humbert's double double hypergeometric functions;
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