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Another method for Padmanabham's transformation formula for Exton's triple hypergeometric series X_8

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The object of this note is to derive Padmanabham's transformation formula for Exton's triple hypergeometric series X_8 by using a different method from that of Padmanabham's. An interesting special case is also pointed out.

Abstract

The object of this note is to derive Padmanabham's transformation formula for Exton's triple hypergeometric series X_8 by using a different method from that of Padmanabham's. An interesting special case is also pointed out.

참고문헌 (11)

  1. P. Appell, "Fonctions Hypergéométriques et Hypersphériques Polynomes D’Hermite" (1926), Gauthier-Villars
  2. Junesang Choi, "Notes on formal manipulations of double series", 대한수학회논문집, 18(4), pp.781~789 (2003), 대한수학회
  3. H. Exton, "Hypergeometric function of three variables", J. Indian Acad. Maths., 4(2), pp.113~119 (1982)
  4. G. H. Hardy, "A chapter from Ramanujan’s notebook", Proc. Cambridge Philos. Soc., 21, pp.492~503 (1923)
  5. J. Kampé de Fériet, "Les fonctions hypergéométriques d’ordre supérieur à deux variables", C. R. Acad. Sci. Paris, 173, pp.401~404 (1921)
  6. P. A. Padmanabham, "Expansions for a multiple hypergeometric function", Ganita, 54(1), pp.17~20 (2003)
  7. C. T. Preece, "The product of two generalized hypergeometric functions", Proc. London Math. Soc., 22, pp.370~380 (1924)
  8. H. M. Srivastava, "Series Associated with the Zeta and Related Functions" (2001), Kluwer Academic Publishers
  9. H. M. Srivastava, "Multiple Gaussian Hypergeometric Series" (1985), Halsted Press
  10. H. M. Srivastava, "A Treatise on Generating Functions" (1984), Halsted Press
  11. H. M. Srivastava, "An integral representation for the product of two Jacobi polynomials", J. London Math. Soc., 12(2), pp.419~425 (1976)

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