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Title: Asymptotics of the generalized Gegenbauer functions of fractional degree
Authors: Liu, Wenjie
Wang, Li-Lian
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-.
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.
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

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