Asymptotics for Gegenbauer–Sobolev orthogonal polynomials associated with non-coherent pairs of measures

Abstract

Inner products of the type 〈f, g〉_S=〈f, g〉_ψ0+〈f^′, g^′〉_ψ1, where one of the measures ψ₀ or ψ₁ is the measure associated with the Gegenbauer polynomials, are usually referred to as Gegenbauer–Sobolev inner products. This paper deals with some asymptotic relations for the orthogonal polynomials with respect to a class of Gegenbauer–Sobolev inner products. The inner products are such that the associated pairs of symmetric measures (ψ₀, ψ₁) are not within the concept of symmetrically coherent pairs of measures.