Results 31 to 40 of about 19,826 (260)

q-deformed harmonic and Clifford analysis and the q-Hermite and Laguerre polynomials [PDF]

, 2010
We define a q-deformation of the Dirac operator, inspired by the one dimensional q-derivative. This implies a q-deformation of the partial derivatives. By taking the square of this Dirac operator we find a q-deformation of the Laplace operator.
Atakishiyev M, Atakishiyev N, Bonatsos D, Brackx F, Brackx F, Ciccoli N, De Bie H, Delanghe R, Dobrogowska A, Exton H, Exton H, F Sommen, Gasper G, Jackson F, K Coulembier, Lavagno A, Truong T, Ubriaco M   +17 more
core   +2 more sources

A New Generalization of mth-Order Laguerre-Based Appell Polynomials Associated with Two-Variable General Polynomials

Mathematics
This paper presents a novel generalization of the mth-order Laguerre and Laguerre-based Appell polynomials and examines their fundamental properties. By establishing quasi-monomiality, we derive key results, including recurrence relations, multiplicative
Waseem Ahmad Khan, Khidir Shaib Mohamed, Francesco Aldo Costabile, Shahid Ahmad Wani, Alawia Adam   +4 more
doaj   +1 more source

Generating Functions for Products of Special Laguerre 2D and Hermite 2D Polynomials

, 2015
The bilinear generating function for products of two Laguerre 2D polynomials Lm;n(z; z0) with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials.
Wünsche, Alfred
core   +1 more source

A conjecture on Exceptional Orthogonal Polynomials [PDF]

, 2012
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials.
A. González-López, A. Ronveaux, A. Ronveaux, A. Turbiner, B. Midya, C. Quesne, C. Quesne, C. Quesne, C.-L. Ho, C.-L. Ho, D. Dutta, D. Dutta, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, D. Gómez-Ullate, David Gómez-Ullate, F.A. Grünbaum, G. Szegő, J.F. Cariñena, J.M. Fellows, L.E. Gendenshtein, M.G. Krein, M.M. Crum, N. Kamran, Niky Kamran, P. Lesky, R. Sasaki, Robert Milson, S. Bochner, S. Odake, S. Odake, S. Odake, S.Y. Dubov, V.B. Uvarov, V.E. Adler, W.N. Everitt, Y. Grandati   +42 more
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An exploratory study on bivariate extended $ q $-Laguerre-based Appell polynomials with some applications

AIMS Mathematics
In this paper, we employed the $ q $-Bessel Tricomi functions of zero-order to introduce bivariate extended $ q $-Laguerre-based Appell polynomials. Then, the bivariate extended $ q $-Laguerre-based Appell polynomials were established in the sense of ...
Mohra Zayed, Waseem Ahmad Khan, Cheon Seoung Ryoo, Ugur Duran   +3 more
doaj   +1 more source

Some Identities on Laguerre Polynomials in Connection with Bernoulli and Euler Numbers

Discrete Dynamics in Nature and Society, 2012
We study some interesting identities and properties of Laguerre polynomials in connection with Bernoulli and Euler numbers. These identities are derived from the orthogonality of Laguerre polynomials with respect to inner product ∫⟨𝑓,𝑔⟩=∞0𝑒−𝑥2𝑓(𝑥)𝑔(𝑥)𝑑𝑥.
Dae San Kim, Taekyun Kim, Dmitry V. Dolgy   +2 more
doaj   +1 more source

Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics, 2021
Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials.
Pedro J. Miana, Natalia Romero
doaj   +1 more source

Laguerre-type Bell polynomials

International Journal of Mathematics and Mathematical Sciences, 2006
We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite ...
P. Natalini, P. E. Ricci
doaj   +1 more source

Studies on the Method of Orthogonal Collocation IV. Laguerre and Hermite Orthogonal Collocation Method

Journal of King Saud University: Engineering Sciences, 2000
Differential equations for which the zeros of Laguerre and Hermite polynomials are suitable collocation points are identified. It is shown that the equations representing tubular reactors with axial dispersion can be solved efficiently using the zeros of
M.A. Soliman
doaj   +1 more source

On differential equations for Sobolev-type Laguerre polynomials

, 1998
We obtain all spectral type differential equations satisfied by the Sobolev-type Laguerre polynomials. This generalizes the results found in 1990 by the first and second author in the case of the generalized Laguerre polynomials defined by T.H ...
Bavinck, H., Koekoek, J., Koekoek, R.
core   +2 more sources