SUMMATION FORMULAS DERIVED FROM THE SRIVASTAVA’S TRIPLE HYPERGEOMETRIC SERIES HC
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Srivastava noticed the existence of three additional complete triple hypergeometric functions HA, HB and HC 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 HA and HC. Here we are also aiming at presenting two unified summation formulas (actually, including 62 ones) for some reducible cases of Srivastava’s HC with the help of generalized Dixon’s theorem and generalized Whipple’s theorem on the sum of a 3F2 obtained earlier by Lavoie et al.. Some special cases of our results are also considered.
Abstract
Srivastava noticed the existence of three additional complete triple hypergeometric functions HA, HB and HC 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 HA and HC. Here we are also aiming at presenting two unified summation formulas (actually, including 62 ones) for some reducible cases of Srivastava’s HC with the help of generalized Dixon’s theorem and generalized Whipple’s theorem on the sum of a 3F2 obtained earlier by Lavoie et al.. Some special cases of our results are also considered.
참고문헌 (9)
- W. N. Bailey, "Generalized Hypergeometric Series" (1935), Cambridge University Press
- Yong Sup Kim, "Note on Srivastava's triple hypergeometric series $H_A$ and $H_C$", 대한수학회논문집, 18(3), pp.581~586 (2003), 대한수학회
- G. Lauricella, "Sulle funzioni ipergeometriche a piu variabli", Rend. Circ. Mat. Palermo, pp.111~158 (1893)
- J. L. Lavoie, "Generalizations of Watson’s theorem on the sum of a 3F2", Indian J. Math., 34(1), pp.23~32 (1992)
- J. L. Lavoie, "Generalizations of Whipple’s theorem on the sum of a 3F2", J. Comput. Appl. Math., 72(2), pp.293~300 (1996)
- J. L. Lavoie, "Generalizations of Dixon’s theorem on the sum of a 3F2", Math. Comp., 62(205), pp.267~276 (1994)
- A. K. Rathie, "Further results on Srivastava’s triple hypergeometric series HA and HC", Indian J. Pure Appl. Math., 35(8), pp.991~1002 (2004)
- H. M. Srivastava, "Series Associated with the Zeta and Related Functions" (2001), Kluwer Academic Publishers
- H. M. Srivastava, "A Treatise on Generating Functions" (1984), Ellis Horwood Ltd.