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Full-Text Articles in Special Functions
Some Quadratic Transformations And Reduction Formulas Associated With Hypergeometric Functions, M. I. Qureshi, M. Kashif Khan
Some Quadratic Transformations And Reduction Formulas Associated With Hypergeometric Functions, M. I. Qureshi, M. Kashif Khan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we construct four summation formulas for terminating Gauss’ hypergeometric series having argument “two" and with the help of our summation formulas. We establish two quadratic transformations for Gauss’ hypergeometric function in terms of finite summation of combination of two Clausen hypergeometric functions. Further, we have generalized our quadratic transformations in terms of general double series identities as well as in terms of reduction formulas for Kampé de Fériet’s double hypergeometric function. Some results of Rathie-Nagar, Kim et al. and Choi-Rathie are also obtained as special cases of our findings.
Extension Formulas Of Lauricella’S Functions By Applications Of Dixon’S Summation Theorem, Ahmed A. Atash
Extension Formulas Of Lauricella’S Functions By Applications Of Dixon’S Summation Theorem, Ahmed A. Atash
Applications and Applied Mathematics: An International Journal (AAM)
The aim of this research paper is to obtain two extension formulas for the first and second kind of Lauricella’s functions of three variables with the help of generalized Dixon’s summation theorem, which was obtained by Lavoie et al. In addition to this, two extension formulas for the second and third kind of Appell’s functions are obtained as a consequence of the above mentioned results . Furthermore, some transformation formulas involving Exton’s double hypergeometric series are obtained as an applications of our main results.