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  • 1 Chung Yuan Christian University Department of Applied Mathematics Chung-Li 32023 Taiwan, Republic of China
  • 2 Center for General Education, Mackay Medicine, Nursing and Management College Taipei City 11260 Taiwan, Republic of China
  • 3 University of Victoria Department of Mathematics and Statistics Victoria British Columbia V8W 3R4 Canada
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In this paper, the authors investigate the linearization problems associated with two families of generalized Lauricella polynomials of the first and second kinds. By means of their multiple integral representations, it is shown how one can linearize the product of two different members of each of these two families of the generalized Lauricella polynomials. Upon suitable specialization of the main results presented in this paper, the corresponding integral representations are deduced for such familiar classes of multivariable hypergeometric polynomials as (for example) the Lauricella polynomials FA(r) in r variables, the Appell polynomials F2 in two variables and the multivariable Laguerre polynomials. Each of these integral representations, which are derived as special cases of the main results in this paper, may also be viewed as a linearization relationship for the product of two different members of the associated family of multivariable hypergeometric polynomials.

  • Appell, P. et Kampé de Fériet, J., Fonctions Hypergéométriques et Hypersphériques; Polynômes d’Hermite, Gauthier-Villars, Paris, 1926.

    Kampé de Fériet J , '', in Fonctions Hypergéométriques et Hypersphériques; Polynômes d’Hermite , (1926 ) -.

    • Search Google Scholar
  • Chan, W.-C. C., Chen, K.-Y. and Srivastava, H. M., Certain classes of generating functions for the jacobi and related hypergeometric polynomials, Comput. Math. Appl., 44 (2002), 1539–1556.

    Srivastava H M , 'Certain classes of generating functions for the jacobi and related hypergeometric polynomials ' (2002 ) 44 Comput. Math. Appl. : 1539 -1556.

    • Search Google Scholar
  • González, B., Matera, J. and Srivastava, H. M., Some q-generating functions and associated generalized hypergeometric polynomials, Math. Comput. Modelling, 34 (1/2) (2001), 133–175.

    Srivastava H M , 'Some q-generating functions and associated generalized hypergeometric polynomials ' (2001 ) 34 Math. Comput. Modelling : 133 -175.

    • Search Google Scholar
  • Humbert, P., La function \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$W_{k,\mu _1 ,\mu _2 , \ldots ,\mu _n } \left( {x_1 ,x_2 , \ldots ,x_n } \right)$$ \end{document}, C.R. Acad. Sci. Paris, 171 (1920), 428–430.

    Humbert P , 'La function \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$W_{k,\mu _1 ,\mu _2 , \ldots ,\mu _n } \left( {x_1 ,x_2 , \ldots ,x_n } \right)$$ \end{document} ' (1920 ) 171 C.R. Acad. Sci. Paris : 428 -430.

    • Search Google Scholar
  • Khan, M. A. and Shukla, A. K., On Laguerre polynomials of several variables, Bull. Calcutta Math. Soc., 89 (1997), 155–164.

    Shukla A K , 'On Laguerre polynomials of several variables ' (1997 ) 89 Bull. Calcutta Math. Soc. : 155 -164.

    • Search Google Scholar
  • Khan, M. A. and Shukla, A. K., A note on Laguerre polynomials of m-variables, Bull. Greek Math. Soc., 40 (1998), 113–117.

    Shukla A K , 'A note on Laguerre polynomials of m-variables ' (1998 ) 40 Bull. Greek Math. Soc. : 113 -117.

    • Search Google Scholar
  • Lin, S.-D., Chao, Y.-S. and Srivastava, H. M., Some families of hypergeometric polynomials and associated integral representations, J. Math. Anal. Appl., 294 (2004), 399–411.

    Srivastava H M , 'Some families of hypergeometric polynomials and associated integral representations ' (2004 ) 294 J. Math. Anal. Appl. : 399 -411.

    • Search Google Scholar
  • Lin, S.-D., Liu, S.-J. and Srivastava, H. M., Some families of hypergeometric polynomials and associated multiple integral representations, Integral Transforms Spec. Funct., 22 (2011), 403–414.

    Srivastava H M , 'Some families of hypergeometric polynomials and associated multiple integral representations ' (2011 ) 22 Integral Transforms Spec. Funct. : 403 -414.

    • Search Google Scholar
  • Lin, S.-D., Liu, S.-J., Lu, H.-C. and Srivastava, H. M., Integral representations for generalized Bedient polynomials and the generalized Cesáro polynomials, Appl. Math. Comput., 218 (2011), 1330–1341.

    Srivastava H M , 'Integral representations for generalized Bedient polynomials and the generalized Cesáro polynomials ' (2011 ) 218 Appl. Math. Comput. : 1330 -1341.

    • Search Google Scholar
  • Liu, S.-J., Chyan, C.-J., Lu, H.-C. and Srivastava, H. M., Multiple integral representations for some families of hypergeometric and other polynomials, Math. Comput. Modelling, 54 (2011), 1420–1427.

    Srivastava H M , 'Multiple integral representations for some families of hypergeometric and other polynomials ' (2011 ) 54 Math. Comput. Modelling : 1420 -1427.

    • Search Google Scholar
  • Liu, S.-J., Chyan, C.-J., Lu, H.-C. and Srivastava, H. M., Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella functions, Integral Transforms Spec. Funct., 23 (2012), 539–549.

    Srivastava H M , 'Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella functions ' (2012 ) 23 Integral Transforms Spec. Funct. : 539 -549.

    • Search Google Scholar
  • Liu, S.-J., Lin, S.-D., Lu, H.-C. and Srivastava, H. M., Linearization of the products of the Carlitz-Srivastava polynomials of the first and second kinds via their integral representations, Appl. Math. Comput., 219 (2013), 4545–4550.

    Srivastava H M , 'Linearization of the products of the Carlitz-Srivastava polynomials of the first and second kinds via their integral representations ' (2013 ) 219 Appl. Math. Comput. : 4545 -4550.

    • Search Google Scholar
  • Magnus, W., Oberhettinger, F. and Soni, R. P., Formulas and Theorems for the Special Functions of Mathematical Physics, Third Enlarged Edition, Springer-Verlag, New York, 1966.

    Soni R P , '', in Formulas and Theorems for the Special Functions of Mathematical Physics , (1966 ) -.

    • Search Google Scholar
  • Srivastava, H. M., A contour integral involving Fox’s H-function, Indian J. Math., 14 (1972), 1–6.

    Srivastava H M , 'A contour integral involving Fox’s H-function ' (1972 ) 14 Indian J. Math. : 1 -6.

    • Search Google Scholar
  • Srivastava, H. M., A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math., 117 (1985), 183–191.

    Srivastava H M , 'A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials ' (1985 ) 117 Pacific J. Math. : 183 -191.

    • Search Google Scholar
  • Srivastava, H. M. and Garg, M., Some integrals involving a general class of polynomials and the multivariable H-function, Rev. Roumaine Phys., 32 (1987), 685–692.

    Garg M , 'Some integrals involving a general class of polynomials and the multivariable H-function ' (1987 ) 32 Rev. Roumaine Phys. : 685 -692.

    • Search Google Scholar
  • Srivastava, H. M. and Karlsson, P. W., Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.

    Karlsson P W , '', in Multiple Gaussian Hypergeometric Series , (1985 ) -.

  • Srivastava, H. M., Lin, S.-D., Liu, S.-J. and Lu, H.-C., Integral representations for the Lagrange polynomials, Shively’s Pseudo-Laguerre polynomals, and the generalized Bessel polynomials, Russian J. Math. Phys., 19 (2012), 121–130.

    Lu H-C , 'Integral representations for the Lagrange polynomials, Shively’s Pseudo-Laguerre polynomals, and the generalized Bessel polynomials ' (2012 ) 19 Russian J. Math. Phys. : 121 -130.

    • Search Google Scholar
  • Srivastava, H. M. and Manocha, H. L., A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.

    Manocha H L , '', in A Treatise on Generating Functions , (1984 ) -.

  • Srivastava, H. M., Özarslan, M. A. and Kaanoglu, C., Some families of generating functions for a certain class of three-variable polynomials, Integral Transforms Spec. Funct. 21 (2010), 885–896.

    Kaanoglu C , 'Some families of generating functions for a certain class of three-variable polynomials ' (2010 ) 21 Integral Transforms Spec. Funct. : 885 -896.

    • Search Google Scholar
  • Whittaker, E. T. and Watson, G. N., A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions, Fourth Edition, Cambridge University Press, Cambridge, London and New York, 1927.

    Watson G N , '', in A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions , (1927 ) -.

    • Search Google Scholar