Results 61 to 70 of about 31,835 (251)

More on the q-oscillator algebra and q-orthogonal polynomials

, 1995
Properties of certain $q$-orthogonal polynomials are connected to the $q$-oscillator algebra. The Wall and $q$-Laguerre polynomials are shown to arise as matrix elements of $q$-exponentials of the generators in a representation of this algebra.
Atakishiyev N, Atakishiyev N M, Atakishiyev N M, Biedenharn L C, Floreanini R, Floreanini R, Floreanini R, Floreanini R, Gasper G, J LeTourneux, Kalnins E G, Koekoek R, L Vinet, MacFarlane A J, R Floreanini, Zhedanov A S, Zhedanov A S   +16 more
core   +2 more sources

Vortices and Polynomials [PDF]

, 2009
The relationship between point vortex dynamics and the properties of polynomials with roots at the vortex positions is discussed. Classical polynomials, such as the Hermite polynomials, have roots that describe the equilibria of identical vortices on the
Ablowitz, Ablowitz, Adler, Adler, Adler, Airault, Airault, Aref, Aref, Aref, Barashenkov, Bartman, Brézin, Burchnall, Bureau, Chen, Clarkson, Clarkson, Clarkson, Clarkson, Clarkson, Clarkson, Crum, Dubov, Duistermaat, Filipuk, Flaschka, Fokas, Forrester, Gardner, Gromak, Kadtke, Kajiwara, Kajiwara, Kajiwara, Kanzieper, Lewis, Loutsenko, Loutsenko, Nakamura, Noumi, Noumi, O'Neil, Oblomkov, Okamoto, Olver, Stieltjes, Stieltjes, Umemura, Umemura, Veselov, Veselov, Vorob'ev, Yablonskii   +53 more
core   +3 more sources

Generalized Hermite polynomials

Journal of Computational and Applied Mathematics, 1975
AbstractHermite polynomials of several variables are defined by a generalization of the Rodrigues formula for ordinary Hermite polynomials. Several properties are derived, including the differential equation satisfied by the polynomials and their explicit expression. An application is given.
openaire   +2 more sources

Higher order matching polynomials and d-orthogonality [PDF]

, 2009
We show combinatorially that the higher-order matching polynomials of several families of graphs are d-orthogonal polynomials. The matching polynomial of a graph is a generating function for coverings of a graph by disjoint edges; the higher-order ...
Drake, Dan
core   +2 more sources

Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states

, 2012
We define quaternionic Hermite polynomials by analogy with two families of complex Hermite polynomials. As in the complex case, these polynomials consatitute orthogonal families of vectors in ambient quaternionic $L^2$-spaces. Using these polynomials, we
Adler S. L., Ebbinghaus H. D., K. Thirulogasanthar, S. Twareque Ali, Torgasev A.   +4 more
core   +1 more source

Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from Differential Equations and Location of Their Zeros

Mathematics, 2018
In this paper, we study differential equations arising from the generating functions of Hermit Kamp e ´ de F e ´ riet polynomials. Use this differential equation to give explicit identities for Hermite Kamp e ´ de F
Cheon Seoung Ryoo
doaj   +1 more source

On a class of Humbert-Hermite polynomials

Novi Sad Journal of Mathematics, 2019
A unified presentation of a class of Humbert’s polynomials in two variables which generalizes the well known class of Gegenbauer, Humbert, Legendre, Chebycheff, Pincherle, Horadam, Kinnsy, Horadam-Pethe, Djordjević , Gould, Milovanović and Djordjević, Pathan and Khan polynomials and many not so called ’named’ polynomials ...
Pathan, M. A., Khan, Waseem
openaire   +3 more sources

Some properties for 2-variable modified partially degenerate Hermite (MPDH) polynomials derived from differential equations and their zeros distributions

AIMS Mathematics, 2023
The 2-variable modified partially degenerate Hermite (MPDH) polynomials are the subject of our study in this paper. We found basic properties of these polynomials and obtained several types of differential equations related to MPDH polynomials.
Gyung Won Hwang, Cheon Seoung Ryoo, Jung Yoog Kang   +2 more
doaj   +1 more source

Deformed Complex Hermite Polynomials [PDF]

, 2014
We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along the way we also
Ali, S. Twareque, Ismail, Mourad E. H., Shah, Nurisya M.   +2 more
core  

Stimulated Raman Scattering with Optical Vortex Beams

Advanced Photonics Research, EarlyView.
This study presents exact analytical expressions for stimulated Raman scattering with Laguerre‐Gaussian beams, revealing signal dependence on topological and hyperbolic momentum. The results provide a theoretical foundation for coherent Raman imaging and detecting orbital angular momentum of light via structured light in nonlinear optics.
Minhaeng Cho
wiley   +1 more source