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http://dx.doi.org/10.4134/CKMS.2010.25.2.185

SUMMATION FORMULAS DERIVED FROM THE SRIVASTAVA'S TRIPLE HYPERGEOMETRIC SERIES HC  

Kim, Yong-Sup (DEPARTMENT OF MATHEMATICS EDUCATION WONKWANG UNIVERSITY)
Rathie, Arjun Kumar (DEPARTMENT OF MATHEMATICS EDUCATION VEDANT COLLEGE OF ENGINEERING AND TECHNOLOGY)
Choi, June-Sang (DEPARTMENT OF MATHEMATICS EDUCATION DONGGUK UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.25, no.2, 2010 , pp. 185-191 More about this Journal
Abstract
Srivastava noticed the existence of three additional complete triple hypergeometric functions $H_A$, $H_B$ and $H_C$ of the second order in the course of an extensive investigation of Lauricella's fourteen hypergeometric functions of three variables. In 2004, Rathie and Kim obtained four summation formulas containing a large number of very interesting reducible cases of Srivastava's triple hypergeometric series $H_A$ and $H_C$. Here we are also aiming at presenting two unified summation formulas (actually, including 62 ones) for some reducible cases of Srivastava's $H_C$ with the help of generalized Dixon's theorem and generalized Whipple's theorem on the sum of a $_3F_2$ obtained earlier by Lavoie et al.. Some special cases of our results are also considered.
Keywords
triple hypergeometric series $H_A$ and $H_C$; Appell's function; generalized Dixon's theorem; generalized Whipple's theorem;
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Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 0
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