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GENERALIZATION OF WATSON'S THEOREM FOR DOUBLE SERIES

Kim, Yong-Sup;Rathie, Arjun-K.;Park, Chan-Bong;Lee, Chang-Hyun

  • Published : 2004.07.01

Abstract

In 1965, Bhatt and Pandey obtained the Watson's theorem for double series by using Dioxon's theorem on the sum of a $_3F_2$. The aim of this paper is to derive twenty three results for double series closely related to the Watson's theorem for double series obtained by Bhatt and Pandey. The results are derived with the help of twenty three summation formulas closely related to the Dison's theorem on the sum of a $_3F_2$ obtained in earlier work by Lavoie, Grondin, Rathie and Arora.

Keywords

the generalized Kampe de Feriet function;double series;Watson's theorem;Dioxon's theorem

References

  1. Cambridge Tracts in Math. Gerneralized Hypergeometric series W. N. Bailey
  2. Ganita v.16 On certain sums and transformations of hypergeometric functions of two variables of superior order R. C. Bhatt;R. C. Pandey
  3. C. R. Acad. Sci. Paris v.173 Les Fonctions hypergeometriques d'ordre superieur a deux variables J. Kampe de Feriet
  4. Math. Comp. v.62 Generalizations of Dixon's theorem on the sum of a $_3$F$_2$ J. L. Lavoie;F. Grondin;A. K. Rathie;K. Arora
  5. J. London Math. Soc. (2) v.12 An integral representation for the product of two Jacobi polynomials H. M. Srivastava;R. Panda https://doi.org/10.1112/jlms/s2-12.4.419