| Title |
The orthogonality of Al-Salam-Carlitz polynomials for complex parameters |
| Authors |
Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO, Xu W. |
| External publication |
Si |
| Means |
Front. In Orthogonal Polynomials and Q-ser. |
| Scope |
Capítulo de un Libro |
| Nature |
Científica |
| Web |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85045709988&doi=10.1142%2f9789813228887_0008&partnerID=40&md5=e2bc7898bca937be968528fd8b2e3e0e |
| Publication date |
01/01/2018 |
| Scopus Id |
2-s2.0-85045709988 |
| DOI |
10.1142/9789813228887_0008 |
| Abstract |
In this chapter, we study the orthogonality conditions satisfied by Al-Salam-Carlitz polynomials U(a) n (x; q) when the parameters a and q are not necessarily real nor "classical", i.e., the linear functional u with respect to such a polynomial sequence is quasi-definite and not positive definite. We establish orthogonality on a simple contour in the complex plane which depends on the parameters. In all cases we show that the orthogonality conditions characterize the Al-Salam- Carlitz polynomials U(a) n (x; q) of degree n up to a constant factor. We also obtain a generalization of the unique generating function for these polynomials. © 2018 by World Scientific Publishing Co. Pte. Ltd. All Rights Reserved. |
| Keywords |
Discrete measure; Q-difference operator; Q-integral representation; Q-orthogonal polynomials |
| Universidad Loyola members |
|
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