A unified theory of polynomial expansions and their applications involving Clebsch-Gordan type linearization relations and Neumann series
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 \textit{A. W. Niukkanen} [J. Phys. A 16, 1813-1825 (1983; Zbl 0527.33001); ibid. 17, L731-L736 (1984; Zbl 0556.33004); ibid. 18, 1399-1418 (1985; Zbl 0582.33008)] and the author [J. Phys. A 18, 227-234 (1985; Zbl 0544.33006) and ibid. 3079-3085 (1985; Zbl 0556.33003); ibid. 20, 847-855 (1987; Zbl 0591.33003)], which provides an interesting and useful unification of numerous families of special functions in one and more variables, encountered 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 derivation of various Clebsch-Gordon type linearization relations involving products of several Jacobi or Laguerre polynomials, but also to associated Neumann expansions in series of the Bessel functions \(J_v(z)\) and \(I_v(z)\) and of their suitable products.
scientific article; zbMATH DE number 4050000
scientific article