Results 21 to 30 of about 1,199 (184)

Some Integrals Involving q-Laguerre Polynomials and Applications

Abstract and Applied Analysis, 2013
The integrals involving multivariate q-Laguerre polynomials and then auxiliary ones are studied. In addition, the representations of q-Hermite polynomials by q-Laguerre polynomials and their related integrals are given.
Jian Cao
doaj   +1 more source

Truncated Hermite polynomials

, 2022
We define the family of truncated Hermite polynomials $P_{n}left(x;zright) $, orthogonal with respect to the linear functional [Lleft[ pright] = int_{-z}^{z} pleft( xright) e^{-x^{2}} ,dx. ] The connection of $P_{n}left( x;zright) $ with the Hermite and Rys polynomials is stated.
Dominici, Diego, Marcellán, Francisco
openaire   +3 more sources

q-Hermite Polynomials and Classical Orthogonal Polynomials [PDF]

Canadian Journal of Mathematics, 1996
AbstractWe use generating functions to express orthogonality relations in the form of q-beta. integrals. The integrand of such a q-beta. integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials ...
Berg, Christian, Ismail, Mourad E. H.
openaire   +2 more sources

Context-Free Grammars for Several Triangular Arrays

Axioms, 2022
In this paper, we present a unified grammatical interpretation of the numbers that satisfy a kind of four-term recurrence relation, including the Bell triangle, the coefficients of modified Hermite polynomials, and the Bessel polynomials.
Roberta Rui Zhou, Jean Yeh, Fuquan Ren
doaj   +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

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

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