Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X12 and X17
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In the theory of hypergeometricfunctions of one or several variables, a remarkable amount ofmathematicians's concern has been given to develop theirtransformation formulas and summation identities. Here we aim atgeneralizing the following transformation formula for the Exton'striple hypergeometric series X12 and X17 : (1+2z)-bX17(a, b, c3; c1, c2, 2c3; x, y/1+2z, 4z/1+2z) = X12(a, b; c1, c2, ,c3 + 1/2; x, y, z2). The results are derived with the help of two general hypergeometricidentities for the terminating 2F1(2) series which were veryrecently obtained by Kim et al. Four interesting results closelyrelated to the Exton's transformation formula are also chosen, amongten, to be derived as special illustrative cases of our mainfindings. The results easily obtained in this paper are simple and(potentially) useful.
Abstract
In the theory of hypergeometricfunctions of one or several variables, a remarkable amount ofmathematicians's concern has been given to develop theirtransformation formulas and summation identities. Here we aim atgeneralizing the following transformation formula for the Exton'striple hypergeometric series X12 and X17 : (1+2z)-bX17(a, b, c3; c1, c2, 2c3; x, y/1+2z, 4z/1+2z) = X12(a, b; c1, c2, ,c3 + 1/2; x, y, z2). The results are derived with the help of two general hypergeometricidentities for the terminating 2F1(2) series which were veryrecently obtained by Kim et al. Four interesting results closelyrelated to the Exton's transformation formula are also chosen, amongten, to be derived as special illustrative cases of our mainfindings. The results easily obtained in this paper are simple and(potentially) useful.
참고문헌 (13)
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