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Exton’s triple hypergeometric series associated with the Kampé de Fériet function

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By means of formal power series method and series rearrangement technique, the authors are to derive certain reducibility of Kampe de Feriet functions for the hypergeometric functions X_4, X_7, and X_8 of three variables defined earlier by Exton.

Abstract

By means of formal power series method and series rearrangement technique, the authors are to derive certain reducibility of Kampe de Feriet functions for the hypergeometric functions X_4, X_7, and X_8 of three variables defined earlier by Exton.

참고문헌 (14)

  1. "P. Appell et J. Kampe de Feriet, Fonctions Hypergeometriques et Hyperspheriques Polynomes D'Hermite" (1926), Gauthier Villars
  2. 최준상, "Remark on two results by Padmanabham for exton's triple hypergeometric series X_8", 호남수학학술지, 27(4), pp.603~608 (2005), 호남수학회
  3. H. Exton, "Hypergeometric function of three variables", Indian Acad. Maths, 4(2), pp.113~119 (1982)
  4. J. Kamp, "Les fonctions hypergeometriques d'ordre superieur a deux variables", C. R. Acad. Sci. Paris, 173, pp.401~404 (1921)
  5. Y.S. Kim, "Y.S. Kim, On certain reducibility of Kampe de Feriet function", Honam Math. Soc, 31(2), pp.167~176 (2009)
  6. G. Lauricella, "Sulle funzioni ipergeometriche a piu variabili", Rend. Circ. Mat. Palermo, 7, pp.111~158
  7. P. A. Padmanabham, "Expansions for a multiple hypergeometric function", Ganita, 54(1), pp.17~20 (2003)
  8. C. T. Preece, "The product of two generalized hypergeometric functions", Proc. Lon- don Math. Soc, 22, pp.370~380 (1924)
  9. E. D. Rainville, "Special functions" (1960), Macmillan Company
  10. S. Saran, "Hypergeometric functions of three variables" (1954), Ganita 5
  11. L. J. Slater, "Generalized hypergeometric functions" (1966), Cambridge Univ
  12. 최준상, "Series Associated with the Zeta and Related Functions" (2001), Kluwer Academic Publishers
  13. H. M. Srivastava, "Multiple Gaussian Hypergeometric Series" (1985), Halsted Press
  14. H. M. Srivastava, "A Treatise on Generating Functions" (1984), Halsted Press

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