Email this article Inner product and Gegenbauer polynomials in Sobolev space
- Authors: Boudref M.A.1
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Affiliations:
- University of Bouira
- Issue: Vol 27, No 138 (2022)
- Pages: 150-163
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/295010
- DOI: https://doi.org/10.20310/2686-9667-2022-27-138-150-163
- ID: 295010
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Abstract
In this paper we consider the system of functions G r,n α (x) r∈N, n=0,1,… which is orthogonal with respect to the Sobolev-type inner product on (-1, 1) and generated by orthogonal Gegenbauer polynomials. The main goal of this work is to study some properties related to the system φ k,r (x) k≥0 of the functions generated by the orthogonal system G r,n α (x) of Gegenbauer functions. We study the conditions on a function f(x) given in a generalized Gegenbauer orthogonal system for it to be expandable into a generalized mixed Fourier series of the form f x ~ k=0 r-1 f k -1 x+1 k k! + k=r ∞ G r,k α f φ r,k α x , as well as the convergence of this Fourier series. The second result of this paper is the proof of a recurrence formula for the system φ k,r (x) k≥0 . We also discuss the asymptotic properties of these functions, and this represents the latter result of our contribution.
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About the authors
Mohamed Ahmed Boudref
University of Bouira
Email: m.boudref@univ-bouira.dz
PhD of Mathematics, Director of the LIMPAF Mathematics and Computer Science Laboratory, Lecturer of the High Mathematics Department 10000 Drissi Yahia Bouira St., Bouira, Algeria
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