Generalizations and Specializations of Generating Functions for Jacobi, Gegenbauer, Chebyshev and Legendre Polynomials with Definite Integrals

نویسندگان

  • HOWARD S. COHL
  • CONNOR MACKENZIE
  • H. S. COHL
  • H. M. SRIVASTAVA
چکیده

In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer polynomials through extension a two element sequence of generating functions for Jacobi polynomials. Specializations of generating functions are accomplished through the re-expression of Gauss hypergeometric functions in terms of less general functions. Definite integrals which correspond to the presented orthogonal polynomial series expansions are also given. Mathematics subject classification (2010): 33C45, 05A15, 33C05, 34L10, 30E20.

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تاریخ انتشار 2013