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

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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.

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.

참고문헌 (11)

  1. L. U. Ancarani, "Derivatives of any order of the con uent hypergeo-metric function 1F1(a; b; z) with respect to the parameter a or b", J. Math Phys, 49, pp.063508~063516 (2008)
  2. L. U. Ancarani, "Derivatives of any order of the Gaussian hypergeo-metric function 2F1(a; b; c; z) with respect to parameter a, b and c", J. Phys. A: Math. Theor, 42, pp.395208~ (2009)
  3. L. U. Ancarani, "Derivatives of any order of the hypergeometric function pFq(a1; : : : ; ap; b1; : : : ; bq; z) with respect to the parameters ai and bi", J. Phys. A: Math. Theor, 43, pp.085210~ (2010)
  4. G. Gasper, "Basic Hypergeometric Series" (2004), Cambridge University Press
  5. H. A. Ghany, "q-derivative of basic hypergeometric series with respect to parameters", Int. J. Math. Anal, 3(33-36), pp.1617~1632 (2009)
  6. V. B. Kuznetsov, "Factorisation of Macdonald polynomials, Sym-metries and integrability of difference equations", pp.370~384 (1996), Cambridge Univ. Press
  7. V. Sahai, "nth-order q-derivatives of multivariable q-hypergeometric series with respect to parameters", Asian-Eur. J. Math., 7(2), pp.1450019~ (2014)
  8. V. Sahai, "Derivatives of Appell functions with respect to parameters", J. Inequal. Spec. Funct., 6(3), pp.1~16 (2015)
  9. H. M. Srivastava, "Generalized Neumann expansions involving hypergeometric func-tions", Proc. Cambridge Philos. Soc., 63, pp.425~429 (1967)
  10. H. M. Srivastava, "Certain q-polynomial expansions for functions of several variables", IMA J. Appl. Math., 30, pp.315~323 (1983)
  11. H. M. Srivastava, "Multiple Gaussian Hypergeometric Series" (1985), John Wiley and Sons

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