A curious q-analogue of Hermite polynomials
Copyright policy )A curious q-analogue of Hermite polynomials
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.
17 pages
- Universität Wien Austria
- University of Lyon System France
- Universität Wien Austria
- UNIVERSITE JEAN MONNET SAINT-ETIENNE France
- University of Vienna Austria
Matchings, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], q-Hermite polynomials, Theoretical Computer Science, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Classical Analysis and ODEs (math.CA), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, 05A05, 05A15, 33C45, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials, Al-Salam–Chihara polynomials, 101029 Mathematische Statistik, Hermite polynomials, Al-Salam--Chihara polynomials, 101029 Mathematical statistics, 004, Computational Theory and Mathematics, Mathematics - Classical Analysis and ODEs, Touchard–Riordan formula, Combinatorics (math.CO), Catalan numbers, Hankel determinants, Touchard-Riordan formula
Matchings, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], q-Hermite polynomials, Theoretical Computer Science, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Classical Analysis and ODEs (math.CA), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, 05A05, 05A15, 33C45, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials, Al-Salam–Chihara polynomials, 101029 Mathematische Statistik, Hermite polynomials, Al-Salam--Chihara polynomials, 101029 Mathematical statistics, 004, Computational Theory and Mathematics, Mathematics - Classical Analysis and ODEs, Touchard–Riordan formula, Combinatorics (math.CO), Catalan numbers, Hankel determinants, Touchard-Riordan formula
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