| Summary: | 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.
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