Results 41 to 50 of about 32,513 (203)
, 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. +4 more
core +1 more source
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
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
A model for the continuous q-ultraspherical polynomials
, 1995 We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the $q ...
Askey R. A. +4 more
core +2 more sources
On summable, positive Poisson-Mehler kernels built of Al-Salam--Chihara and related polynomials [PDF]
, 2012 Using special technique of expanding ratio of densities in an infinite series of polynomials orthogonal with respect to one of the densities, we obtain simple, closed forms of certain kernels built of the so called Al-Salam-Chihara (ASC) polynomials.
Bożejko M. +2 more
core +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. +3 more
openaire +1 more source
Coupling Fluid Neutrals to Gyrokinetic Plasma Dynamics for Edge and SOL Turbulence Simulations
Contributions to Plasma Physics, EarlyView.ABSTRACT Accurate modeling of turbulent transport in magnetic confinement fusion devices requires extending first‐principles gyrokinetic simulations from the core to the edge and scrape‐off layer (SOL), where additional physics—particularly plasma–neutrals interactions—must be included.
Sabine Ogier‐Collin +3 more
wiley +1 more source
MathematicsThe 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
Extension of Stein’s lemma derived by using an integration by differentiation technique
Examples and Counterexamples, 2022 We extend Stein’s lemma for averages that explicitly contain the Gaussian random variable at a power. We present two proofs for this extension of Stein’s lemma, with the first being a rigorous proof by mathematical induction.
Konstantinos Mamis
doaj +1 more source