Title of article :
TWO FORMULAS CONTIGUOUS TO A QUADRATIC TRANSFORMATION DUE TO KUMMER WITH AN APPLICATION
Author/Authors :
Choi, Junesang Dongguk University - Department of Mathematics, Korea , Rathie, Arjun K. Central University of Kerala, Riverside Transit Campus - School of Mathematical Physical Sciences - Department of Mathematics, India
Abstract :
We aim at establishing two identities contiguous to Kummer’s transformation: (1 − z)2^−aF1[ 1/2a, 1/2a + 1/2 ; b + 1/2 ; (z/1 − z)^2] = 2F1 [ a, 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 , Kampe de Feriet function , Kummer’s second theorem , Dixon and Whipple’s summation theorems
Journal title :
Hacettepe Journal Of Mathematics and Statistics
Journal title :
Hacettepe Journal Of Mathematics and Statistics
