CERTAIN GENERAL DOUBLE-SERIES IDENTITIES WITH THEIR APPLICATIONS
Chaudhary Wali Mohd., M. I. Qureshi and M. Kashif Khan
Department of Applied Sciences and Humanities, Faculty of Engineering and Technology
Jamia Millia Islamia (A Central University), New Delhi-110025 (India)
Email:email@example.com; firstname.lastname@example.org; email@example.com
(Received: March 30, 2021; Revised : April 22, 2021)
The aim of this paper is to obtain some general double-series identities involving bounded sequence of complex numbers with suitable convergence conditions. We then employ these identities to establish several quadratic transformations for the product of exponential function and Goursat’s functions 2F2[a, m + d; 2a ± j, d; 2z] and also transformations for the Kampé de Fériet’s function F G:2;0 H:2;0[2z, −z].
2020 Mathematical Sciences Classification: Primary 33C05; Secondary 33C20.
Keywords and Phrases: Generalized hypergeometric function; Kummer’s function; Goursat’s function; Kampé de Fériet’s function; Quadratic transformations; Bounded sequence.