Two Hypergeometric Generating Relations Via Gould's Identity and Their Generalizations

Abstract

In the present paper, we have obtained hypergeometric generating relations associated with two hypergeometric polynomials of one variable $H_n^{(\alpha,\beta)}(x;m)$ and $\mathscr{B}_n^{(\alpha,\beta)}(x;m,\lambda,\mu)$ with their independent demonstrations via Gould's identity.As applications,some well known and new generating relations are deduced.Using bounded sequences, further generalizations of two main hypergeometric generating relations have also been given for two generalized polynomials $S_n^{(\alpha,\beta)}(x;m)$ and $T_n^{(\alpha,\beta)}(x;m,\lambda,\mu)$.