Results 31 to 40 of about 32,202 (209)

A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND \(q\)-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS

Ural Mathematical Journal, 2023
In this paper, we consider the following \(\mathcal{L}\)-difference equation $$\Phi(x) \mathcal{L}P_{n+1}(x)=(\xi_nx+\vartheta_n)P_{n+1}(x)+\lambda_nP_{n}(x),\quad n\geq0,$$where \(\Phi\) is a monic polynomial (even), \(\deg\Phi\leq2\), \(\xi_n ...
Yahia Habbachi
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

Hermite Polynomials

Journal of Combinatorial Theory, Series A, 2000
In this paper it is proved, that a so-called Hermite transform which transforms \(x^n\), \(n\in\mathbb{N}_0\) into the \(n\)-th Hermite polynomial \(H_n(x)\) preserves the property of a polynomial having only real roots. (In the proof there is referred to a next paragraph, but it does not exist).
openaire   +2 more sources

Properties of Multivariable Hermite Polynomials in Correlation with Frobenius–Genocchi Polynomials

Mathematics, 2023
The evolution of a physical system occurs through a set of variables, and the problems can be treated based on an approach employing multivariable Hermite polynomials.
Shahid Ahmad Wani, Georgia Irina Oros, Ali M. Mahnashi, Waleed Hamali   +3 more
doaj   +1 more source

Fourier transform of hn(x + p)hn(x − p)

International Journal of Mathematics and Mathematical Sciences, 1997
We evaluate Fourier transform of a function with Hermite polynomials involved. An elementary proof is based on a combinatorial formula for Hermite polynomials.
Mourad E. H. Ismail, Krzystztof Stempak
doaj   +1 more source

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

Bounding hermite matrix polynomials

Mathematical and Computer Modelling, 2004
The main object under investigation is the family of the Hermite matrix orthogonal polynomials \(\{H_n(x,A)\}_{n\geq 0}\), which depends on the matrix parameter \(A\) having all its eigenvalues in the open right half plane. The main result (Theorem 1) states that \[ \| H_{2n}(x,A)\| \leq \frac{(2n+1)!
Defez, E., Hervás, A., Jódar, L., Law, A.   +3 more
openaire   +1 more source

Impact of Uncertain Parameters on Navier–Stokes Equations With Heat Transfer via Polynomial Chaos Expansion

International Journal for Numerical Methods in Fluids, EarlyView.
This study investigates the impact of uncertain parameters on Navier–Stokes equations coupled with heat transfer using the Intrusive Polynomial Chaos Method (IPCM). Sensitivity equations are formulated for key input parameters, such as viscosity and thermal diffusivity, and solved numerically using the Finite Element‐Volume method.
N. Nouaime, B. Després, M. A. Puscas, C. Fiorini   +3 more
wiley   +1 more source

Partial Derivative Equations and Identities for Hermite-Based Peters-Type Simsek Polynomials and Their Applications

Mathematics
The objective of this paper is to investigate Hermite-based Peters-type Simsek polynomials with generating functions. By using generating function methods, we determine some of the properties of these polynomials.
Eda Yuluklu
doaj   +1 more source