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Some finite integrals involving the product of Bessel function with Jacobi and Laguerre polynomials

Nabiullah Khan|Mohd Ghayasuddin|Shorab Wali Khan
대한수학회 (The Korean Mathematical Society)|2018.07|대한수학회논문집 (Communications of the KMS)|제33권 제3호|pp. 1013-1024

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참고문헌

키워드

Bessel functionLaguerre polynomialWhittaker functionJacobi polynomial
주제분류수학

초록

The main object of this paper is to set up two (conceivably) valuable double integrals including the multiplication of Bessel function with Jacobi and Laguerre polynomials, which are given in terms of Srivastava and Daoust functions. By virtue of the most broad nature of the function included therein, our primary findings are equipped for yielding an extensive number of (presumably new) fascinating and helpful results involving orthogonal polynomials, Whittaker functions, sine and cosine functions.

Abstract

The main object of this paper is to set up two (conceivably) valuable double integrals including the multiplication of Bessel function with Jacobi and Laguerre polynomials, which are given in terms of Srivastava and Daoust functions. By virtue of the most broad nature of the function included therein, our primary findings are equipped for yielding an extensive number of (presumably new) fascinating and helpful results involving orthogonal polynomials, Whittaker functions, sine and cosine functions.

참고문헌 (20)

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  8. J. Edward, "A Treatise On The Integral Calculus. Vol. II" (1922), Chelsea Publishing Company
  9. S. Jain, "Integrals involving Laguerre type polynomials and Bessel functions", Far East J. Math. Sci., 100(Issue-1), pp.965~976 (2016)
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  15. Saiful Rahman Mondal, "Certain unified integral formulas involving the generalized modified k-Bessel function of first kind", 대한수학회논문집, 32(1), pp.47~53 (2017), 대한수학회
  16. E. D. Rainville, "Special Functions" (1960), The Macmillan Co.
  17. H. M. Srivastava, "Certain generalized Neumann expansions associated with the Kampede Feriet function", Nederl. Akad. Wetensch. Proc. Ser. A 72=Indag. Math., 31(31), pp.449~457 (1969)
  18. H. M. Srivastava, "A treatise on generating functions, Ellis Horwood Series: Mathematics and its Applications" (1984), Ellis Horwood Ltd.
  19. E. T. Whittaker, "An expression of certain known functions as generalized hypergeometric functions", Bull. Amer. Math. Soc., 10(3), pp.125~134 (1903)[DOI]
  20. E. T. Whittaker, "A Course of Modern Analysis, reprint of the fourth (1927) edition" (1996), Cambridge Mathematical Library, Cambridge University Press

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