Generalized Gegenbauer orthogonal polynomials

Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials

We study the asymptotic behaviour of the monic orthogonal polynomials with respect to the Gegenbauer-Sobolev inner product (f, g)S = 〈f, g〉 + λ〈f ′, g′〉 where 〈f, g〉 = ∫ 1 −1 f(x)g(x)(1 − x 2)α−1/2dx with α > −1/2 and λ > 0. The asymptotics of the zeros and norms of these polynomials is also established. The study of the orthogonal polynomials with respect to the inner products that involve der...

Orthogonal Polynomials for the Oscillatory-gegenbauer Weight

This is a continuation of our previous investigations on polynomials orthogonal with respect to the linear functional L : P → C, where L = ∫ 1 −1 p(x) dμ(x), dμ(x) = (1 − x2)λ−1/2 exp(iζx) dx, and P is a linear space of all algebraic polynomials. Here, we prove an extension of our previous existence theorem for rational λ ∈ (−1/2, 0], give some hypothesis on three-term recurrence coefficients, ...

Some identities involving generalized Gegenbauer polynomials

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

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...