- Hacettepe Journal of Mathematics and Statistics
- Vol: 40 Issue: 6
- TWO FORMULAS CONTIGUOUS TO A QUADRATIC TRANSFORMATION DUE TO KUMMER WITH AN APPLICATION
TWO FORMULAS CONTIGUOUS TO A QUADRATIC TRANSFORMATION DUE TO KUMMER WITH AN APPLICATION
Authors : Junesang Choi , arjun K. Rathie
Pages : 885-894
View : 10 | Download : 8
Publication Date : 2011-06-01
Article Type : Research
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