Please use this identifier to cite or link to this item:
|Title:||Asymptotics of the generalized Gegenbauer functions of fractional degree||Authors:||Liu, Wenjie
|Keywords:||Science::Mathematics||Issue Date:||2020||Source:||Liu, W. & Wang, L. (2020). Asymptotics of the generalized Gegenbauer functions of fractional degree. Journal of Approximation Theory, 253, 105378-. https://dx.doi.org/10.1016/j.jat.2020.105378||Project:||MOE2018-T2-1-059
|Journal:||Journal of Approximation Theory||Abstract:||The generalized Gegenbauer functions of fractional degree (GGF-Fs), denoted by rG (λ) ν (x) (right GGF-Fs) and lG (λ) ν (x) (left GGF-Fs) with x ∈ (−1, 1), λ > −1/2 and real ν ≥ 0, are special functions (usually non-polynomials), which are defined upon the hypergeometric representation of the classical Gegenbauer polynomial by allowing integer degree to be real fractional degree. Remarkably, the GGF-Fs become indispensable for optimal error estimates of polynomial approximation to singular functions, and have intimate relations with several families of nonstandard basis functions recently introduced for solving fractional differential equations. However, some properties of GGF-Fs, which are important pieces for the analysis and applications, are unknown or under explored. The purposes of this paper are twofold.||URI:||https://hdl.handle.net/10356/154539||ISSN:||0021-9045||DOI:||10.1016/j.jat.2020.105378||Rights:||© 2020 Elsevier Inc. All rights reserved.||Fulltext Permission:||none||Fulltext Availability:||No Fulltext|
|Appears in Collections:||SPMS Journal Articles|
Updated on May 20, 2022
Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.