Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO, Xu W.
Si
Front. In Orthogonal Polynomials and Q-ser.
Capítulo de un Libro
Científica
01/01/2018
2-s2.0-85045709988
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.
Discrete measure; Q-difference operator; Q-integral representation; Q-orthogonal polynomials