## SOME QUADRATIC TRANSFORMATIONS MOTIVATED BY THE WORK OF KUMMER AND THEIR GENERALIZATIONS

## SOME QUADRATIC TRANSFORMATIONS MOTIVATED BY THE WORK OF KUMMER AND THEIR GENERALIZATIONS

*M. I. Qureshi, K. A. Quarishi, M. K. Khan*

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## Abstract

In this paper, we construct two quadratic transformations influenced by the work of Kummer and application of hypergeometric summation theorems of argument “two”. Further, we establish some generalizations of these quadratic transformations in terms of double series identities having the bounded sequence. Three reduction formulas for Kamp ́e de F ́eriet’s double hypergeometric functions are also obtained as special cases.

## Keywords

Generalized hypergeometric function, Hypergeometric summation theorems, Quadratic transformations, Bounded sequence.