Fourier coefficients for Laguerre–Sobolev type orthogonal polynomials

Abstract

Purpose – In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials. Design/methodology/approach – To do that, the authors use the connection formulas between Sobolev polynomials and classical Laguerre polynomials, as well as the well-known Fourier coefficients for these latter. Findings – Then, the authors compute explicit formulas for the Fourier coefficients of some families of Laguerre–Sobolev type orthogonal polynomials over a finite interval. The authors also describe an oscillatory region in each case as a reasonable choice for approximation purposes. Originality/value – In order to take the first step in the study of constructive methods by using Sobolev polynomials, this paper deals with Fourier coefficients for certain families of polynomials orthogonal with respect to the Sobolev type inner product. As far as the authors know, this particular problem has not been addressed in the existing literature.

Keywords

• Fourier coefficients
• Sobolev type orthogonal polynomials
• Laguerre polynomials