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A curious $q$-analogue of Hermite polynomials

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.
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https://hal.archives-ouvertes.fr/hal-00863436
Contributor : Jiang Zeng Connect in order to contact the contributor
Submitted on : Wednesday, September 18, 2013 - 8:51:02 PM
Last modification on : Saturday, September 24, 2022 - 3:36:05 PM

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  • HAL Id : hal-00863436, version 1
  • ARXIV : 0905.0228

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Johann Cigler, Jiang Zeng. A curious $q$-analogue of Hermite polynomials. J. Combin. Theory Ser. A, 2011, 118 (1), pp.9--26. ⟨hal-00863436⟩

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