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SOME BILATERAL GENERATING FUNCTIONS INVOLVING THE CHAN-CHYAN-SRIVASTAVA POLYNOMIALS AND SOME GENERAL CLASSES OF MULTIVARIABLE POLYNOMIALS

  • 투고 : 2012.12.14
  • 발행 : 2013.10.31

초록

Recently, Liu et al. [Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella function, Integral Transform Spec. Funct. 23 (2012), no. 7, 539-549] investigated, in several interesting papers, some various families of bilateral generating functions involving the Chan-Chyan-Srivastava polynomials. The aim of this present paper is to obtain some bilateral generating functions involving the Chan-Chyan-Sriavastava polynomials and three general classes of multivariable polynomials introduced earlier by Srivastava in [A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), 1-6], [A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 117 (1985), 183-191] and by Kaano$\breve{g}$lu and $\ddot{O}$zarslan in [Two-sided generating functions for certain class of r-variable polynomials, Mathematical and Computer Modelling 54 (2011), 625-631]. Special cases involving the (Srivastava-Daoust) generalized Lauricella functions are also given.

키워드

참고문헌

  1. W.-C. Chan, C.-J. Chyan, and H. M. Srivastava, The Lagrange polynomials in several variables, Integral Transform Spec. Funct. 12 (2001), 139-148. https://doi.org/10.1080/10652460108819340
  2. K.-Y. Chen, S.-J. Liu, and H. M. Srivastava, Some new results for the Lagrange polynomials in several variables, ANZIAM J. 49 (2007), 243-258. https://doi.org/10.1017/S1446181100012815
  3. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions. Vols. 1-3, McGraw-Hill, New York, 1953.
  4. E. Erkus and O. Duman, and H. M. Srivastava, Statistical approximation of certain positive linear operators constructed by means of the Chan-Chyan-Srivastava polynomials, Appl. Math. Comput. 182 (2006), 213-222. https://doi.org/10.1016/j.amc.2006.01.090
  5. E. Erkus and H. M. Srivastava, A unified presentation of some families of multivariable polynomials, Integral Transform Spec. Funct. 17 (2006), 267-273. https://doi.org/10.1080/10652460500444928
  6. H.W. Gould and A. T. Hopper, Operational formulas connected with two generalizations of Hermite polynomials, Duke Math. J. 29 (1962), 51-63. https://doi.org/10.1215/S0012-7094-62-02907-1
  7. C. Kaanoglu and M. A. Ozarslan, Two-sided generating functions for certain class of r-variable polynomials, Mathematical and Computer Modelling 54 (2011), 625-631. https://doi.org/10.1016/j.mcm.2011.03.006
  8. H. L. Krall and O. Frink, A new class of orthogonal polynomials: the Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100-115. https://doi.org/10.1090/S0002-9947-1949-0028473-1
  9. S.-J. Liu, Bilateral generating function for the Lagrange polynomials and the Lauricella functions, Integral Transform Spec. Funct. 20 (2009), 519-527. https://doi.org/10.1080/10652460802568291
  10. S.-J. Liu, C.-J. Chyan, H.-C. Lu, and H. M. Srivastava, Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella functions, Integral Transform Spec. Funct. 23 (2012), no. 7, 539-549. https://doi.org/10.1080/10652469.2011.610152
  11. S.-J. Liu, S.-D. Lin, H. M. Srivastava, and M.-M. Wong, Bilateral generating functions for the Erku¸s-Srivastava polynomials and the generalized Lauricella functions, Appl. Math. Comput. 218 (2012), 7685-7693. https://doi.org/10.1016/j.amc.2012.01.005
  12. H. M. Srivastava, A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), 1-6.
  13. H. M. Srivastava, A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 117 (1985), 183-191. https://doi.org/10.2140/pjm.1985.117.183
  14. H. M. Srivastava and M. Garg, Some integrals involving a general class of polynomials and multivariable H-function, Rev. Roumanie Phys. 32 (1987), 685-692.
  15. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press(Ellis Horwoor Limited)/ John Wiley and Sons, Chichester/New York, 1985.
  16. H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press(Ellis Horwoor Limited)/ John Wiley and Sons, Chichester, New York, Brisbane and Toronto, 1984.
  17. H. M. Srivastava and M. A. Ozarslan, and C. Kaanoglu, Some families of generating functions for a certain class of three-variable polynomials, Integral Transform Spec. Funct. 21 (2010), no. 12, 885-896. https://doi.org/10.1080/10652469.2010.481439
  18. H. M. Srivastava and N. P. Singh, The integration of certain products of the multivariable H-function with a general class of polynomials, Rend. Circ. Mat. Palermo 32 (1983), no. 2, 157-187. https://doi.org/10.1007/BF02844828
  19. G. Szego, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., Vol. 23, Fourth edition, Amer. Math. Soc., Providence, Rhode Island, 1975.