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The orthogonality of Al-Salam-Carlitz polynomials for complex parameters



Howard Cohl, Wenqing Xu, Roberto Costas-Santos


In this contribution, 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'. 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 $U_n^(a)}(x;q)$ of degree $n$ up to a constant factor. We also obtain a generalization of the unique generating function for these polynomials.
Frontiers in Orthogonal Polynomials and q-Series, Contemporary Mathematics and its Applications: Monographs, Expositions and Lecture Notes, Vol. 1
Publisher Info
World Scientific Publishing Company, Hackensack, NJ


$q$-orthogonal polynomials, $q$-difference operator, $q$-integralrepresentation, discrete measure


Cohl, H. , Xu, W. and Costas-Santos, R. (2018), The orthogonality of Al-Salam-Carlitz polynomials for complex parameters, World Scientific Publishing Company, Hackensack, NJ, [online],, (Accessed June 20, 2024)


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Created January 31, 2018, Updated May 4, 2021