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

Authors : Junesang CHOİ ,  arjun K RATHİE

Pages : 885-894

View : 21 | Download : 14

Publication Date : 2011-06-01

Article Type : Research Paper

Abstract :We aim at establishing two identities contiguous to Kummer’s transformation :insert ignore into journalissuearticles values(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 3F2insert ignore into journalissuearticles values(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, Kummers second theorem, Dixon and Whipples summation theorems, 2000 AMS Classification Primary 33 B 20