NEW RESULTS FOR THE SERIES 2F2(x) WITH AN APPLICATION

Title & Authors
NEW RESULTS FOR THE SERIES 2F2(x) WITH AN APPLICATION
Choi, Junesang; Rathie, Arjun Kumar;

Abstract
The well known quadratic transformation formula due to Gauss: $\small{(1-x)^{-2a}{_2F_1}\[{{a,b;}\\\hfill{21}{2b;}}\;-\frac{4x}{(1-x)^2}\}$$\small{]}$$\small{={_2F_1}\[{{a,a-b+\frac{1}{2};}\\\hfill{65}{b+\frac{1}{2};}}\;x^2\}$$\small{]}$$\small{}$ plays an important role in the theory of (generalized) hypergeometric series. In 2001, Rathie and Kim have obtained two results closely related to the above quadratic transformation for $\small{_2F_1}$. Our main objective of this paper is to deduce some interesting known or new results for the series $\small{_2F_1(x)}$ by using the above Gauss's quadratic transformation and its contiguous relations and then apply our results to provide a list of a large number of integrals involving confluent hypergeometric functions, some of which are (presumably) new. The results established here are (potentially) useful in mathematics, physics, statistics, engineering, and so on.
Keywords
Gamma function;hypergeometric function;generalized hypergeometric function;Gauss's quadratic transformation formula for $\small{_2F_1}$;Watson's summation theorem for $\small{_3F_2(1)}$;
Language
English
Cited by
1.
Generalized hypergeometric function identities at argument±1, Integral Transforms and Special Functions, 2014, 25, 11, 909
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