Some families of generating functions associated with the stirling numbers of the second kind

[摘要] The object of this paper is to present a systematic introduction to (and several interesting applications of) a general result on generating functions (associated with the Stirling numbers of the second kind) for a fairly wide variety of special functions and polynomials in one, two, and more variables. The main results given below are shown to apply not only to the classical orthogonal polynomials including, for example, the Jacobi polynomials (which contain, as their special cases, the Gegenbauer or ultraspherical polynomials, the Legendre or spherical polynomials, and the Chebyshev polynomials of the first and second kinds) and the Laguerre polynomials, and to their various extensions and generalizations studied in recent years, but indeed also to a class of generalized hypergeometric functions, the Lauricella polynomials in several variables, and the familiar Lagrange polynomials which arise in certain problems in statistics. Relevant connections of some of these families of generating functions with various known results are also indicated. (C) 2000 Academic Press.

[发布日期] 2000-11-15

[关键词] generating functions;Stirling numbers;Jacobi polynomials;Gegenbauer (or ultraspherical) polynomials;Legendre (or spherical) polynomials;Chebyshev polynomials;Laguerre polynomials;generalized hypergeometric functions;Lauricella polynomials;Lagrange polynomials;Konhauser biorthogonal polynomials;Srivastava-Singhal polynomials