APPELL'S FUNCTION F1 AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X9
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In the theory of hypergeometric functions of one or several variables,a remarkable amount of mathematicians's concern has been given to develop their transformation formulas and summation identities. Here we aim at presenting ex-plicit expressions (in a single form) of the following weighted Appell's function F_1:(1 + 2x)^-a (1 + 2z)^-b F1(c, a, b ; 2c + j ;4x/(1 + 2x),4z/(1 + 2z)(j = 0;±1,...,±5)in terms of Exton's triple hypergeometric X_9. The results are derived with the help of generalizations of Kummer's second theorem very recently provided by Kim et al. A large number of very interesting special cases including Exton's result are also given.
Abstract
In the theory of hypergeometric functions of one or several variables,a remarkable amount of mathematicians's concern has been given to develop their transformation formulas and summation identities. Here we aim at presenting ex-plicit expressions (in a single form) of the following weighted Appell's function F_1:(1 + 2x)^-a (1 + 2z)^-b F1(c, a, b ; 2c + j ;4x/(1 + 2x),4z/(1 + 2z)(j = 0;±1,...,±5)in terms of Exton's triple hypergeometric X_9. The results are derived with the help of generalizations of Kummer's second theorem very recently provided by Kim et al. A large number of very interesting special cases including Exton's result are also given.
참고문헌 (16)
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