Two-index multidimensional Gegenbauer polynomials and their integral representations

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

A new Extension of Gegenbauer Matrix Polynomials and Their Properties

The aim of this paper is to define and study of the Gegenbauer matrix polynomials of two variables. An explicit representation, a three-term matrix recurrence relations, differential recurrence relations and hypergeometric matrix representation for the Gegenbauer matrix polynomials of two variables are given. The Gegenbauer matrix polynomials are solutions of the matrix differential equations a...

Gegenbauer Polynomials and Semiseparable Matrices

In this paper, we develop a new O(n logn) algorithm for converting coefficients between expansions in different families of Gegenbauer polynomials up to a finite degree n. To this end, we show that the corresponding linear mapping is represented by the eigenvector matrix of an explicitly known diagonal plus upper triangular semiseparable matrix. The method is based on a new efficient algorithm ...

Integral representations for multivariate logarithmic polynomials

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logari...

Information entropy of Gegenbauer polynomials

The information entropy of Gegenbauer polynomials is relevant since this is related to the angular part of the information entropies of certain quantum mechanical systems such as the harmonic oscillator and the hydrogen atom in D dimensions. We give an effective method to compute the entropy for Gegenbauer polynomials with an integer parameter and obtain the first few terms in the asymptotic ex...