Generalized and mixed type Gegenbauer polynomials

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

Some identities involving generalized Gegenbauer polynomials

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 ...

Zeros of Sobolev Orthogonal Polynomials of Gegenbauer Type

where l > 0 and {dk0, dk1} is a so-called symmetrically coherent pair, with dk0 or dk1 the classical Gegenbauer measure (x−1) dx, a > −1. If dk1 is the Gegenbauer measure, then Sn has n different, real zeros. If dk0 is the Gegenbauer measure, then Sn has at least n−2 different, real zeros. Under certain conditions Sn has complex zeros. Also the location of the zeros of Sn with respect to Gegenb...

A Rodrigues-type formula for Gegenbauer matrix polynomials

This paper centers on the derivation of a Rodrigues-type formula for Gegenbauer matrix polynomial. A connection between Gegenbauer and Jacobi matrix polynomials is given.