## Search

Now showing items 1-10 of 64

#### Uniform convergence of basic Fourier-Bessel series on a q-linear grid [Article]

(Springer, 2018-09)

We study Fourier-Bessel series on a q-linear grid, defined as expansions in complete q-orthogonal systems constructed with the third Jackson q-Bessel function, and obtain sufficient conditions for uniform convergence. The ...

#### On the orthogonality of q-classical polynomials of the Hahn class [Article]

(2012)

The central idea behind this review article is to discuss in a unified sense the orthogonality of all possible polynomial solutions of the q-hypergeometric dif ference equation on a q-linear lattice by means of a qualitative ...

#### On recurrence relations for radial wave functions for the N-th dimensional oscillators and hydrogenlike atoms: analytical and numerical study [Article]

(2006)

Using a general procedure for finding recurrence relations for hypergeometric functions and polynomials introduced by Cardoso et al. [J. Phys. A 36 (2003), 2055-2068] we obtain some new recurrence relations for the ...

#### On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on R [Article]

(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, ...

#### On the Krall-type polynomials on q-quadratic lattices [Article]

(Elsevier, 2011-08)

In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. ...

#### Recurrence relations for connection coefficients between q-orthogonal polynomials of discrete variables in the non-uniform lattice X(s) = q2s [Article]

(Institute of Physics, 1996-11-21)

We obtain the structure relations for q-orthogonal polynomials in the exponential lattice q 2s and from that we construct the recurrence relation for the connection coe cients between two families of polynomials belonging ...

#### Distribution of zeros of discrete and continuous polynomials from their recurrence relation [Article]

(Elsevier, 2002-05-25)

The hypergeometric polynomials in a continous or a discrete variable, whose canonical forms are the so-called classical orthogonal polynomial systems, are ob jects which naturally appear in a broad range of physical and ...

#### WKB approximation and Krall-Type orthogonal polynomials [Article]

(Springer, 1998-10)

We give an uni ed approach to the Krall-type polynomials orthogonal with respect to a positive measure consisting of an absolutely continuous one \perturbed" by the addition of one or more delta Dirac functions. Some ...

#### The q-Racah-Krall-type polynomials [Article]

(Elsevier, 2012-08-01)

In this paper the Krall-type polynomials obtained via the addition of two mass points to the weight function of the standard q-Racah polynomials are introduced. Several algebraic properties of these polynomials are obtained ...

#### On the modification of classical orthogonal polynomials: the symmetric case [Article]

(Springer, 1998-03)

We consider the modifcations of the monic Hermite and Gegenbauer polynomials via the addition of one point mass at the origin. Some properties of the resulting polynomials are studied: three-term recurrence relation, ...