Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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NEW SUMMATION FORMULAE FOR THE GENERALIZED HYPERGEOMETRIC FUNCTIONS OF HIGH ORDER

  • Lee, Seung-Woo (Department of Mathematics, Wonkwang University) ;
  • Rathie, Arjun K. (Department of Mathematics, School of Mathematical and Physical Sciences Central University of Kerala Riverside Transit Campus) ;
  • Pandey, Ujjawal (Department of Mathematics, Marudhar Engineering College Raiser Bikaner) ;
  • Kim, Yong-Sup (Department of mathematics Education, Wonkwang University)
  • Received : 2012.08.10
  • Accepted : 2012.08.27
  • Published : 2012.09.25
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Abstract

The aim of this paper is to provide two interesting summation formulae with the argument unity for the generalized hypergeometric function of higher order. The results are obtained with the help of two new summation formulae very recently obtained by Kim et al.. Summation formulae obtained earlier by Carlson and re-derived by Exton turn out to be special cases of our main findings.

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References

  1. B.C. Carlson, Some extensions of Lardner's relations between $_oF_{3}$ and Bessel functions, SIAM J. Math. Anal. 1(1970), No. 2, 232-243. https://doi.org/10.1137/0501021
  2. H. Exton, Multiple Hypergeometric Functions, Ellis Horwood, Chichester, UK, 1996.
  3. H. Exton, Some summation formulae for the generalized hypergeometric function of higher order, J. Comput. Appl. Math. 79 (1997), No. 2, 183-187. https://doi.org/10.1016/S0377-0427(96)00154-9
  4. Y.S. Kim, M.A. Rakha and A.K. Rathie, Extensions of certain classical summation theorems for the series $_2F_{1}$, $_3F_{2}$ and $_4F_{3}$ with applications in Ramanujan's summations, Int. J. Math. Math. Sci. Volume 2010, Article ID 309503, 26 pages, doi: 10.1155/2010/309503, Hindawi Publishing Company.
  5. J.L. Lavoie, F. Grondin and A.K. Rathie, Generalizations of Watson's theorem on the sum of a $_3F_{2}$, Indian J. Math. 32(1992) 23-32.
  6. J.L. Lavoie, F. Grondin and A.K. Rathie, Generalizations of Dixon's theorem on the sum of a $_3F_{2}$, Math. Comp. 63(1994) 367-376.
  7. J.L. Lavoie, F. Grondin and A.K. Rathie, Generalizations of Whipple's theorem on the sum of a $_3F_{2}$, J. Comput. Appl. Math. 72(1996) 293-300. https://doi.org/10.1016/0377-0427(95)00279-0
  8. E.D. Rainville, Special functions, The Macmillan Company, New York, 1960.
  9. L.J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966.
  10. H.M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, London, 2001.
  11. R. Tremblay and B.J. Fugere, Products of two restricted hypergeometric functions, J. Math. Anal. Appl. 198(1996), 844-852. https://doi.org/10.1006/jmaa.1996.0116