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nth-order q-derivatives of Srivastava's General Triple q-hypergeometric Series with Respect to Parameters

  • Sahai, Vivek (Department of Mathematics and Astronomy, Lucknow University) ;
  • Verma, Ashish (Department of Mathematics and Astronomy, Lucknow University)
  • Received : 2016.05.12
  • Accepted : 2016.08.23
  • Published : 2016.09.23

Abstract

We obtain q-derivatives of Srivastava's general triple q-hypergeometric series with respect to its parameters. The particular cases leading to results for three Srivastava's triple q-hypergeometric series $H_{A,q}$, $H_{B,q}$ and $H_{C,q}$ are also considered.

Keywords

References

  1. L. U. Ancarani and G. Gasaneo, Derivatives of any order of the con uent hypergeometric function $_1F_1$(a, b, z) with respect to the parameter a or b, J. Math Phys., 49 (2008)., 063508-16,. https://doi.org/10.1063/1.2939395
  2. L. U. Ancarani and G. Gasaneo, Derivatives of any order of the Gaussian hypergeo- metric function $_2F_1$(a, b, c; z) with respect to parameter a, b and c, J. Phys. A: Math. Theor., 42, (2009) 395208, (10 pp). https://doi.org/10.1088/1751-8113/42/39/395208
  3. L. U. Ancarani and G. Gasaneo, Derivatives of any order of the hypergeometric function $_pF_q(a_1, ... ,a_p; b_1, ... ,b_q; z)$ with respect to the parameters $a_i$ and $b_i$, J. Phys. A: Math. Theor. 43, 085210, (11pp) (2010). https://doi.org/10.1088/1751-8113/43/8/085210
  4. G. Gasper and M. Rahman, Basic Hypergeometric Series, Second edition, Encyclopedia of Mathematics and its Applications, 96, Cambridge University Press, Cambridge, 2004.
  5. H. A. Ghany, q-derivative of basic hypergeometric series with respect to parameters, Int. J. Math. Anal. (Ruse), 3(2009), No. 33-36, pp. 1617-1632.
  6. V. B. Kuznetsov and E. K. Sklyanin, Factorisation of Macdonald polynomials, Sym- metries and integrability of di erence equations (Canterbury, 1996), 370-384, London Math. Soc. Lecture Note Ser., 255, Cambridge Univ. Press, Cambridge, (1999).
  7. V. Sahai and A. Verma, nth-order q-derivatives of multivariable q-hypergeometric series with respect to parameters, Asian-Eur. J. Math., 7(2014), No. 2, 1450019 (29 pages). https://doi.org/10.1142/S1793557114500193
  8. V. Sahai and A. Verma, Derivatives of Appell functions with respect to parameters, J. Inequal. Spec. Funct., 6(2015), No. 3, pp. 1-16.
  9. H. M. Srivastava, Generalized Neumann expansions involving hypergeometric functions, Proc. Cambridge Philos. Soc., 63(1967), pp. 425-429. https://doi.org/10.1017/S0305004100041359
  10. H. M. Srivastava, Certain q-polynomial expansions for functions of several variables, IMA J. Appl. Math., 30(1983), pp. 315-323. https://doi.org/10.1093/imamat/30.3.315
  11. 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.