DOI QR코드

DOI QR Code

GENERALIZED SINGLE INTEGRAL INVOLVING KAMPEÉ DE FÉRIET FUNCTION

  • Kim, Yong Sup (Department of Mathematics Education, Wonkwang University) ;
  • Ali, Shoukat (Department of Mathematics, Govt. Engineering College Bikaner) ;
  • Rathie, Navratna (Department of Mathematics, Rajasthan Technical University)
  • Received : 2011.01.19
  • Accepted : 2011.05.13
  • Published : 2011.06.30

Abstract

The aim of this paper is to obtain twenty five Eulerian type single integrals in the form of a general single integral involving $Kamp\acute{e}$ de $F\acute{e}riet$ function. The results are derived with the help of the generalized classical Watson's theorem obtained earlier by Lavoie, Grondin and Rathie. A few interesting special cases of our main result are also given.

Keywords

References

  1. P. Appell et J. Kampe de Feriet(1926), Fonctions Hypergeometriques et Hyper- spheriques Polynomes d'Hermite, Gauthier-Villars, Paris.
  2. J. Choi, A. K. Rathie, and H. Harsh, Remarks on a summation formula for three variables hypergeometric function $X_8$ and certain hypergeometric transfor- mations, East Asian Math. J. 25 (2009), no. 4, 481-486.
  3. A. Erdelyi et al., Tables of integral transforms, Vol. II, McGraw-Hill, New York, 1954.
  4. H. Exton, Hypergeometric functions of three variables, J. Indian acad. Math. 4 (1982), 113-119.
  5. Y. S. Kim, J. Choi, and A. K. Rathie, Remark on two results by Padmanabham for Exton's triple hypergeometric series $X_8$, Honam Math. J. 27 (2005), no. 4, 603-608.
  6. Y. S. Kim and A. K. Rathie, On an extension formula for the triple hyperge- ometric series $X_8$ due to Exton, Bull. Korean Math. Soc. 44 (2007), no. 4, 743-751. https://doi.org/10.4134/BKMS.2007.44.4.743
  7. Y. S. Kim and A. K. Rathie, Another method for Padmanabham's transformation formula for Exton's triple hypergeometric series $X_8$, Commun. Korean Math. Soc. 24 (2009), no. 4, 517-521. https://doi.org/10.4134/CKMS.2009.24.4.517
  8. 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), no. 1, 23-32.
  9. S. W. Lee and Y. S. Kim, An extension of the triple hypergeometric series by Exton, Honam Math. J. 32 (2010), no. 1, 61-71. https://doi.org/10.5831/HMJ.2010.32.1.061
  10. H. M. Srivastava and P. W. Karlsson(1985), Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester); Wiley, New York, Chichester, Brisbane, and Toronto.
  11. J. Yang, U(n+1) extensions of some basic hypergeometric series identities, Adv. Stud. Contem. Math. 18 (2009), no. 2, 201-218.
  12. C. Zhang and Z. Zhang, Extension of two q- series identities, Adv. Stud. Con- tem. Math. 13 (2006), no. 1, 81-85.