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Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous rela- tions 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 2F1(a1,a2;a3;z) with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters a1,a2 and a3. We also, discussed the existence condition of our formula. The theory of generalized hypergeometric function is fundamental in the field of mathematics and mathematical physics. Most of the functions that occur in the analysis are special cases of the hypergeometric functions. Professor John Wallis in his work Arithmetica Infinitorum (1655), first used the term hypergeometric to denote any series which was beyond the ordinary geometric series. In fact, he studied the series

ON THE COMPUTATIONS OF CONTIGUOUS RELATIONS FOR2F1HYPERGEOMETRIC SERIES

ON THE COMPUTATIONS OF CONTIGUOUS RELATIONS FOR₂F₁HYPERGEOMETRIC SERIES