ON THE COMPUTATIONS OF CONTIGUOUS RELATIONS FOR 2F1 HYPERGEOMETRIC SERIES

Title & Authors
ON THE COMPUTATIONS OF CONTIGUOUS RELATIONS FOR 2F1 HYPERGEOMETRIC SERIES
Rakha, Medhat A.; Ibrahim, Adel K.; Rathie, Arjun K.;

Abstract
Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a general formula joining three Gauss functions of the form $\small{_2F_1}$[$\small{a_1}$, $\small{a_2}$; $\small{a_3}$; z] with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters $\small{a_1}$, $\small{a_2}$ and $\small{a_3}$. We also, discussed the existence condition of our formula.
Keywords
hypergeometric function;contiguous relations;
Language
English
Cited by
1.
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2.
On some new contiguous relations for the Gauss hypergeometric function with applications, Computers & Mathematics with Applications, 2011, 61, 3, 620
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