Abstract
Motivated by their potential for applications in several diverse fields of physical, astrophysical, and engineering sciences, this paper aims at presenting a unified study of various classes of polynomial expansions and multiplication theorems associated with the general multivariable hypergeometric function (studied recently by A. W. Niukkanen and H. M. Srivastava), which provides an interesting and useful unifiation of numerous families of special functions in one and more variables, encoutered naturally (and rather frequently) in many physical, quantum chemical, and quantum mechanical situations. Several interesting applications of these general polynomial expansions are considered, not only in the derivations of various Clebsch-Gordan type linearization relations involving products of several Jacobi or Laguerre polynomials, but also to associated Neumann expansions in series of the Bessel functionsJ v (z) andI v (z) (and of their suitable products).
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Srivastava, H.M. A unified theory of polynomial expansions and their applications involving Clebsch-Gordan type linearization relations and Neumann series. Astrophys Space Sci 150, 251–266 (1988). https://doi.org/10.1007/BF00641720
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DOI: https://doi.org/10.1007/BF00641720