Characterizations of ultraspherical polynomials and their $q$-analogues
Copyright policy )Characterizations of ultraspherical polynomials and their $q$-analogues
The author studies some properties that characterize the ultraspherical polynomials and two of their \(q\)-analogues, namely the symmetric big \(q\)-Jacobi polynomials and the continuous \(q\)-ultraspherical (Roger) polynomials. In fact he improved some previous results by \textit{R. Lasser} and \textit{J. Obermaier} [Proc. Am. Math. Soc. 136, No. 7, 2493--2498 (2008; Zbl 1148.33007)] and \textit{M. E. H. Ismail} and \textit{J. Obermaier} [Can. J. Math. 63, No. 1, 181--199 (2011; Zbl 1214.33010)], respectively.
- TECHNISCHE UNIVERSITAET MUENCHEN Germany
- Technical University of Munich Germany
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), ultraspherical polynomials, characterization theorems, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), ultraspherical polynomials, characterization theorems, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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