A Generalization of Gegenbauer and Laguerre Polynomials

摘要

The authors present extensions of Gegenbauer and Laguerre polynomials to n variables. Several of the properties corresponding to properties of these polynomials when n=1, such as solutions of differential equations, orthogonality, and recursion relations, are shown. Since Legendre and Tchebycheff polynomials are special cases of Gegenbauer polynomials, the results shown also apply in the cases of these polynomials. (Author)