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

We aim at establishing two identities contiguous to Kummer’s transformation :(1 − z)−a2F1" 12a, 12a +12;b +12;z1 − z2#= 2F1a, b ;2b ;2zby 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,

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