DOI QR코드

DOI QR Code

INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HA

  • Received : 2012.01.25
  • Accepted : 2012.03.07
  • Published : 2012.03.25

Abstract

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_A$.

Keywords

References

  1. P. Appell and J. Kampe de Feriet, Fonctions Hypergeometriques et Hyper-spheriques; Polynomes d'Hermite, Gauthier - Villars, Paris, 1926.
  2. J. Choi, A. Hasanov, H. M. Srivastava and M. Turaev, Integral representations for Srivastava's triple hypergeometric functions, Taiwanese J. Math. 15 (2011), 2751-2762. https://doi.org/10.11650/twjm/1500406495
  3. A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcen- dental Functions, Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953.
  4. H. Exton, Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113-119.
  5. A. Hasanov and H. M. Srivastava, Some decomposition formulas associated with the Lauricella function $F_{A}^{(r)}$ and other multiple hypergeometric functions, Appl. Math. Lett. 19 (2006), 113-121. https://doi.org/10.1016/j.aml.2005.03.009
  6. A. Hasanov and H. M. Srivastava, Decomposition formulas associated with the Lauricella multivariable hypergeometric functions, Comput. Math. Appl. 53 (2007), 1119-1128. https://doi.org/10.1016/j.camwa.2006.07.007
  7. A. Hasanov, H. M. Srivastava and M. Turaev, Decomposition formulas for some triple hypergeometric functions, J. Math. Anal. Appl. 324 (2006), 955-969. https://doi.org/10.1016/j.jmaa.2006.01.006
  8. G. Lauricella, Sulle funzioni ipergeometriche a piu variabili, Rend. Circ. Mat. Palermo 7 (1893), 111-158. https://doi.org/10.1007/BF03012437
  9. P. A. Padnanabham, Two results on three variable hypergeometric function, Indian J. Pure Appl. Math. 30 (1999), 1107-1109.
  10. S. Saran, Hypergeometric functions of three variables, Ganita 5 (1954), 71-91.
  11. H. M. Srivastava, Hypergeometric functions of three variables, Ganita 15 (1964), 97-108.
  12. H. M. Srivastava, Some integrals representing triple hypergeometric functions, Rend. Circ. Mat. Palermo 16 (1967), 99-115. https://doi.org/10.1007/BF02844089
  13. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston and London, 2001.
  14. H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
  15. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
  16. H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Hal- sted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.
  17. M. Turaev, Decomposition formulas for Srivastava's hypergeometric function $H_{A}$ on Saran functions, J. Comput. Appl. Math. 233 (2009), 842-846. https://doi.org/10.1016/j.cam.2009.02.050

Cited by

  1. INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HC vol.34, pp.4, 2012, https://doi.org/10.5831/HMJ.2012.34.4.473