Results 51 to 60 of about 32,513 (203)

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

Multiindex Multivariable Hermite Polynomials [PDF]

Mathematical and Computational Applications, 2002
In the present paper multiindex multivariable Hermite polynomials in terms of series and generating function are defined. Their basic properties, differential and pure recurrence relations, differential equations, generating function relations and expansions have been established. Few deductions are also obtained.
openaire   +1 more source

Hermite polynomials and Fibonacci oscillators [PDF]

Journal of Mathematical Physics, 2019
We compute the (q1, q2)-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the (q1, q2)-extension of Jackson derivative. The deformed energy spectrum is also found in terms of these parameters. We conclude that the deformation is more effective in higher excited states.
Andre A. Marinho, Francisco A. Brito
openaire   +2 more sources

Bivariate Poly-analytic Hermite Polynomials [PDF]

Results in Mathematics, 2020
A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical Hilbert space on the two-complex space with respect to the Gaussian measure.
Allal Ghanmi, Khalil Lamsaf
openaire   +3 more sources

Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver

International Journal for Numerical Methods in Fluids, EarlyView.
A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
wiley   +1 more source

Finding identities and q-difference equations for new classes of bivariate q-matrix polynomials

Applied Mathematics in Science and Engineering
This article introduces 2-variable q-Hermite matrix polynomials and delves into their complex representation, unravelling specific outcomes. The exploration encompasses the derivation of insightful identities for the q-cosine and q-sine analogues of the ...
Subuhi Khan, Hassan Ali, Mohammed Fadel
doaj   +1 more source

ARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR COHERENT AND SQUEEZED STATES [PDF]

, 1995
For use in calculating higher-order coherent- and squeezed- state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by $\sum_{n=0}^{\infty}z^{jn+k}H_{jn+k}(x)/(jn+k)!$, for arbitrary integers $j\geq 1$ and
Brandt, D'Ariano, D'Ariano, D'Ariano, D.Rodney Truax, Dodonov, Fisher, Hansen, Kalnins, Kato, Katriel, Katriel, Katriel, Katriel, Magnus, Michael Martin Nieto, Nieto, Wilf   +17 more
core   +2 more sources

Performance Assessment of the Immersed Boundary Method in the Framework of the Moment Representation Lattice Boltzmann Method

International Journal for Numerical Methods in Fluids, EarlyView.
The immersed boundary method (IBM) was coupled with the moment representation lattice Boltzmann method (MR‐LBM), reducing bandwidth requirements compared to population‐based LBM formulations. A systematic assessment of IBM parameters was conducted to quantify their effect on computational performance.
Marco A. Ferrari, Ricardo de Souza, Admilson T. Franco   +2 more
wiley   +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  

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source