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A curious q-analogue of Hermite polynomials |
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| Authors: | Johann Cigler |
| Institution: | a Institut für Mathematik, Universität Wien, A-1090 Wien, Austria b Université de Lyon, Université Lyon 1, Institut Camille Jordan, UMR 5208 du CNRS, 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France |
| Abstract: | Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials. In this paper we consider a new family of q-Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with q-Fibonacci and q-Lucas polynomials. The latter relation yields a generalization of the Touchard-Riordan formula. |
| Keywords: | Hermite polynomials q-Hermite polynomials Al-Salam-Chihara polynomials Hankel determinants Catalan numbers Matchings Touchard-Riordan formula |
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