# ON THE COMPUTATIONS OF CONTIGUOUS RELATIONS FOR 2F1 HYPERGEOMETRIC SERIES

• Rakha, Medhat A. (MATHEMATICS DEPARTMENT COLLEGE OF SCIENCE SUEZ CANAL UNIVERSITY, DEPARTMENT OF MATHEMATICS AND STATISTICS COLLEGE OF SCIENCE SULTAN QABOOS UNIVERSITY) ;
• Ibrahim, Adel K. (MATHEMATICS DEPARTMENT COLLEGE OF SCIENCE SUEZ CANAL UNIVERSITY) ;
• Rathie, Arjun K. (MATHEMATICS DEPARTMENT MIT ENGINEERING COLLEG)
• Published : 2009.04.30

#### 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 $_2F_1$[$a_1$, $a_2$; $a_3$; z] with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters $a_1$, $a_2$ and $a_3$. We also, discussed the existence condition of our formula.

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