SOME QUADRATIC TRANSFORMATIONS MOTIVATED BY THE WORK OF KUMMER AND THEIR GENERALIZATIONS - Qureshi, M.I; Quraishi, Kaleem A; Khan, M. Kashif (TWMS journal of applied and engineering mathematics, 2020)
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 Kampe de Feriet's double hypergeometric functions are also obtained as special cases. Keywords: Generalized hypergeometric function, Hypergeometric summation theorems, Quadratic transformations, Bounded sequence. AMS Subject Classification: Primary 33C05, Secondary 33C20