q-beta integrals and theq-Hermite polynomials
نویسندگان
چکیده
منابع مشابه
Q-Hermite Polynomials and Classical Orthogonal Polynomials
We use generating functions to express orthogonality relations in the form of q-beta integrals. The integrand of such a q-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegő and leads naturally to the Al-Salam-Chihara p...
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Abstract Integrals involving products of Hermite polynomials with the weight factor exp (−x2) over the interval (−∞,∞) are considered. A result of Azor, Gillis and Victor (SIAM J. Math. Anal. 13 (1982) 879–890] is derived by analytic arguments and extended to higher order products. An asymptotic expansion in the case of a product of four Hermite polynomials Hn(x) as n → ∞ is obtained by a discr...
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Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials. In this paper we consider two new q-Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with q-Fibonacci polynomials and the recent works on the combinatorics of the Matrix Ansatz of the PASEP.
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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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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1988
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1988.135.209