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Artículo
On a q-extension of the Hermite polynomials Hn(x) with the continuous orthogonality property on R1
(Sociedad Matemática Mexicana / Springer, 2002-10)
We study a polynomial sequence of q-extensions of the classical Hermite polynomials Hn(x), which satisfi es continuous orthogonality on the whole real line R with respect to the positive weight function. This sequence can ...
Artículo
Mellin transforms for some families of q-polynomials
(Elsevier, 2003-04-01)
By using Ramanujan's q-extension of the Euler integral representation for the gamma function, we derive the Mellin integral transforms for the families of the discrete q-Hermite II, the Al-Salam–Carlitz II, the big q-Laguerre, ...
Artículo
Factorization of the hypergeometric-type difference equation on the non-uniform lattices: dynamical algebra
(Institute of Physics, 2005-01-07)
We argue that one can factorize the difference equation of hypergeometric type on the nonuniform lattices in general case. It is shown that in the most cases of q-linear spectrum of the eigenvalues this directly leads to ...
Artículo
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on R
(Springer, 2005-11)
We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics, based on a q-extension of the classical Hermite polynomials Hn(x), recently introduced by us in [1] R. Alvarez-Nodarse, M. K. Atakishiyeva, ...
Artículo
A q-extension of the generalized Hermite polynomials with the continuous orthogonality property on R
(Academic Publications, 2004)
In this paper we study in detail a q-extension of the generalized Hermite polynomials of Szeg˝o. A continuous orthogonality property on R with respect to the positive weight function is established, a q-difference equation ...