• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.449-454
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• 2007

InIn this paper we consider generalizations of the classical Dixon's theorem and the classical Whipple's theorem on the sum of a $_3F_2$. The results are derived with the help of generalized Watson's theorem obtained earlier by Mitra. A large number of results contiguous to Dixon's and Whipple's theorems obtained earlier by Lavoie, Grondin and Rathie, and Lavoie, Grondin, Rathie and Arora follow special cases of our main findings.

• 대한수학회논문집
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• 제29권4호
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• pp.519-526
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• 2014

A large number of summation and transformation formulas involving (generalized) hypergeometric functions have been developed by many authors. Here we aim at establishing two (presumably) new general hypergeometric transformations. The results are derived by manipulating the involved series in an elementary way with the aid of certain hypergeometric summation theorems obtained earlier by Rakha and Rathie. Relevant connections of certain special cases of our main results with several known identities are also pointed out.

• 호남수학학술지
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• 제37권2호
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• pp.245-252
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• 2015

This paper is in continuation of the paper very recently published [New Laplace transforms of Kummer's confluent hypergeometric functions, Math. Comp. Modelling, 55 (2012), 1068-1071]. In this paper, our main objective is to show one can obtain so far unknown Laplace transforms of three rather general cases of generalized hypergeometric function $_2F_2(x)$ by employing generalized Watson's, Dixon's and Whipple's summation theorems for the series $_3F_2$ obtained earlier in a series of three research papers by Lavoie et al. [5, 6, 7]. The results established in this paper may be useful in theoretical physics, engineering and mathematics.

• 대한수학회논문집
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• 제30권3호
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• pp.191-200
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• 2015

Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Exton [13] presented a very general double generating relation involving products of two Laguerre polynomials. Motivated essentially by Exton's derivation [13], the authors aim to show how one can obtain nineteen new generating relations associated with products of two Laguerre polynomials in the form of a single result. We also consider some interesting and potentially useful special cases of our main findings.

• 호남수학학술지
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• 제36권2호
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• pp.345-355
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• 2014

The main objective of this paper is to obtain a formula containing eleven interesting results for the reducibility of Kamp$\acute{e}$ de F$\acute{e}$riet function. The results are derived with the help of two general results for the series $_2F_1(2)$ very recently presented by Kim et al. Well known Kummer's second theorem and its contiguous results proved earlier by Rathie and Nagar, and Kim et al. follow special cases of our main findings.