Three-term contiguous functional relations for basic hypergeometric series ${}_2 \phi_1$
Commun. Korean Math. Soc. 2005 Vol. 20, No. 2, 395-403
Printed June 1, 2005
Yong Sup Kim, Arjun K. Rathie, Junesang Choi
Wonkwang University, Bikaner University, Dongguk University
Abstract : The authors aim mainly at giving fifteen three-term contiguous relations for the basic hypergeometric series ${}_2 \phi_1$ corresponding to Gauss's contiguous relations for the hypergeometric series ${}_{2}F_{1}$ given in Rainville([6], p.71). They also apply them to obtain two summation formulas closely related to a known $q$-analogue of Kummer's theorem.
Keywords : basic hypergeometric series, $q$-analogue of Kummer's summation theorem, Gauss's summation theorem, Gauss's contiguous relations
MSC numbers : Primary 33C20; Secondary 33D05, 33D
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