대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제24권4호
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  • Pages.517-521
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  • 2009
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ANOTHER METHOD FOR PADMANABHAM'S TRANSFORMATION FORMULA FOR EXTON'S TRIPLE HYPERGEOMETRIC SERIES X8

  • 발행 : 2009.10.31
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초록

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.

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참고문헌

  1. P. Appell et J. Kampe de Feriet, Fonctions Hypergeometriques et Hypersph´eriques Polynomes D'Hermite, Gauthier-Villars, Paris, 1926
  2. J. Choi, Notes on formal manipulations of double series, Commun. Korean Math. Soc. 18 (2003), no. 4, 781–789 https://doi.org/10.4134/CKMS.2003.18.4.781
  3. H. Exton, Hypergeometric function of three variables, J. Indian Acad. Maths. 4 (1982), no. 2, 113–119
  4. G. H. Hardy, A chapter from Ramanujan's notebook, Proc. Cambridge Philos. Soc. 21 (1923), 492–503
  5. J. Kampe de Feriet, Les fonctions hypergeometriques dordre superieur a deux variables, C. R. Acad. Sci. Paris 173 (1921), 401–404
  6. P. A. Padmanabham, Expansions for a multiple hypergeometric function, Ganita 54 (2003), no. 1, 17–20
  7. C. T. Preece, The product of two generalized hypergeometric functions, Proc. London Math. Soc. 22 (1924), 370–380 https://doi.org/10.1112/plms/s2-22.1.370
  8. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001
  9. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester); Wiley, New York, Chichester, Brisbane, and Toronto, 1985
  10. H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester); Wiley, New York, Chichester, Brisbane, and Toronto, 1984
  11. H. M. Srivastava and R. Panda, An integral representation for the product of two Jacobi polynomials, J. London Math. Soc. 12 (1976), no. 2, 419–425 https://doi.org/10.1112/jlms/s2-12.4.419

피인용 문헌

  1. CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5 vol.32, pp.3, 2010, https://doi.org/10.5831/HMJ.2010.32.3.389
  2. AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON vol.32, pp.1, 2010, https://doi.org/10.5831/HMJ.2010.32.1.061
  3. Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X12and X17 vol.54, pp.4, 2014, https://doi.org/10.5666/KMJ.2014.54.4.677
  4. CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8 vol.27, pp.2, 2012, https://doi.org/10.4134/CKMS.2012.27.2.257
  5. Relations between Lauricella’s triple hypergeometric function FA(3)(x,y,z) and Exton’s function X8 vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-1847-2013-34
  6. GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION vol.33, pp.1, 2011, https://doi.org/10.5831/HMJ.2011.33.1.043