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Certain integrals involving ${}_2F_1$, Kamp\'{e} De F\'{e}riet function and Srivastava polynomials

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A remarkably large number of integrals whose integrands are associated, in particular, with a variety of special functions, for example, the hypergeometric and generalized hypergeometric functions have been recorded. Here we aim at presenting certain (presumably) new and (potentially) useful integral formulas whose integrands are involved in a product of ${}_2F_1$, Srivastava polynomials, and Kamp\'{e} de F\'{e}riet functions. The main results are derived with the help of some known definite integrals obtained earlier by Qureshi \emph{et al.} \cite{MI-KA-RP}. Some interesting special cases of our main results are also considered.

Abstract

A remarkably large number of integrals whose integrands are associated, in particular, with a variety of special functions, for example, the hypergeometric and generalized hypergeometric functions have been recorded. Here we aim at presenting certain (presumably) new and (potentially) useful integral formulas whose integrands are involved in a product of ${}_2F_1$, Srivastava polynomials, and Kamp\'{e} de F\'{e}riet functions. The main results are derived with the help of some known definite integrals obtained earlier by Qureshi \emph{et al.} \cite{MI-KA-RP}. Some interesting special cases of our main results are also considered.

참고문헌 (12)

  1. P. Agarwal, "On a new theorem involving the generalized Mellin-Barnes type of contour integrals and Srivastava polynomials", J. Appl. Math. Stat. Inform, 8(2), pp.29~35 (2012)
  2. P. Agarwal, "New theorems involving the generalized Mellin-Barnes type of contour integrals and general class of polynomials", Glob. J. Sci. Frontier Res. Math. Decision Sci, 12(3), pp.15~24 (2012)
  3. M. Chand, "New theorems involving the I-function and general class of polynomials", Glob. J. Sci. Frontier Res. Math. Decision Sci, 12(4), pp.89~99 (2012)
  4. M. I. Qureshi, "Some definite integrals of Gradshteyn-Ryzhik and other integrals", Glob. J. Sci. Frontier Res. Math. Decision Sci, 11(4), pp.75~80 (2011)
  5. L. J. Slater, "Generalized Hypergeometric Functions" (1966), Cambridge University Press
  6. I. N. Sneddon, "The Use of Integral Transforms" (1979), Tata McGraw-Hill
  7. H. M. Srivastava, "A contour integral involving Fox’s H-function", Indian J. Math, 14, pp.1~6 (1972)
  8. H. M. Srivastava, "ltiple Gaussian Hypergeometric Series" (1985), Halsted Press, John Wiley and Sons
  9. H. M. Srivastava, "Some bilateral generating functions for a class of gen-eralized hypergeometric polynomials", J. Reine Angew. Math, 283, pp.284 (1976), 265~274
  10. H. M. Srivastava, "The integration of certain products of the multivariable H-function with a general class of polynomials", Rend. Circ. Mat. Palermo, 32(2), pp.157~187 (1983)
  11. G. Szego, "Orthogonal polynomials", Amer. Math. Soc. Colloq. Publ, 23 (1975), Fourth edi., Amer. Math. Soc
  12. E. M. Wright, "The asymptotic expansion of the generalized Bessel function", Proc. London Math. Soc. (2), 38, pp.257~260 (1935)

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