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arXiv · 1607.01497

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

Yashoverdhan Vyas·Kalpana Fatawat
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Abstract

Recently, Rathie and K{\i}l{\i}\c{c}man (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.

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Yashoverdhan Vyas, Kalpana Fatawat. 2016-07-06. On Some Expansion Theorems Involving Confluent Hypergeometric $_{2}F_{2}(x)$ Polynomial. https://arxiv.org/abs/1607.01497

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