Affiliations: DCCE, IBILCE, UNESP – Universidade Estadual Paulista, 15054-000 São José do Rio Preto, SP, Brazil
Note: [] Corresponding author: A. Sri Ranga, DCCE / IBILCE / UNESP, Rua Cristóvão Colombo, 2265, 15054-000 São José do Rio Preto, SP, Brazil. Tel.: +55 17 3221 2217; Fax: +55 17 3221 2203; E-mail: [email protected].
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.
