More on the q-oscillator algebra and q-orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
q-Coherent pairs and q-orthogonal polynomials
In this paper we introduce the concept of q coherent pair of linear functionals. We prove that if ðu0; u1Þ is a q coherent pair of linear functionals, then at least one of them has to be a q classical linear functional. Moreover, we present the classification of all q coherent pairs of positive definite linear functionals when u0 or u1 is either the little q Jacobi linear functional or the litt...
متن کاملQ-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...
متن کاملA General q-Oscillator Algebra
It is well-known that the Macfarlane-Biedenharn q-oscillator and its generalization has no Hopf structure, whereas the Hong Yan q-oscillator can be endowed with a Hopf structure. In this letter, we demonstrate that it is possible to construct a general q-oscillator algebra which includes the Macfarlane-Biedenharn oscillator algebra and the Hong Yan oscillator algebra as special cases. E-mail ad...
متن کاملOn a q-Deformation of the Discrete Painlevé I equation and q-orthogonal Polynomials
I present a q-analog of the discrete Painlevé I equation, and a special realization of it in terms of q-orthogonal polynomials.
متن کاملLadder Operators for q-orthogonal Polynomials
The q− difference analog of the classical ladder operators is derived for those orthogonal polynomials arising from a class of indeterminate moments problem.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1995
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/28/10/002