On Some Expansion Theorems Involving Confluent Hypergeometric $_{2}F_{2}(x)$ Polynomial

Yashoverdhan Vyas; Kalpana Fatawat

paper

On Some Expansion Theorems Involving Confluent Hypergeometric $_{2} F_{2} (x)$ Polynomial

arXiv:1607.01497

Abstract

Recently, Rathie and Kılıçman (2014) employed Kummer-type transformation for $_{2} F_{2} (a, d + 1; b, d; x)$ to develop certain classes of expansions theorems for $_{2} F_{2} (x)$ hypergeometric polynomial. Our aim is to deduce Kummer-type transformation for $_{2} F_{2} (a, d + 2; b, d; x)$ and utilize it to develop some new expansion theorems for the confluent hypergeometric $_{2} F_{2} (x)$ polynomial. We also obtain a well-known result given by Kim et al. (Integral Transforms Spec. Funct. 23(6); 435-444, 2012) and many other new results as particular cases of our theorems.

10 pages

On Some Expansion Theorems Involving Confluent Hypergeometric 2​F2​(x) Polynomial

Abstract

On Some Expansion Theorems Involving Confluent Hypergeometric $_{2} F_{2} (x)$ Polynomial