TWO FORMULAS CONTIGUOUS TO A QUADRATIC TRANSFORMATION DUE TO KUMMER WITH AN APPLICATION

Year 2011, Volume: 40 Issue: 6, 885 - 894, 01.06.2011

Junesang Choi  arjun K. Rathie

https://izlik.org/JA46GC78RC

Abstract

We aim at establishing two identities contiguous to Kummer’s transformation :(1 − z)−a2F1" 12a, 12a +12;b +12;z1 − z2#= 2F1a, b ;2b ;2z
by using two different methods. They are further applied to prove two summation formulas for the series 3F2(1), closely related to the classical Watson’s theorem due to Lavoie.

Keywords

Gamma function , Hypergeometric function , Generalized hypergeometric function , Kamp´e de F´eriet function , Kummer’s second theorem , Dixon and Whipple’s summation theorems , 2000 AMS Classification: Primary 33 B 20

TWO FORMULAS CONTIGUOUS TO A QUADRATIC TRANSFORMATION DUE TO KUMMER WITH AN APPLICATION

https://izlik.org/JA46GC78RC

Abstract

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