Results 11 to 20 of about 33,296 (252)

Accounting for instrument resolution in the pair distribution functions obtained from total scattering data using Hermite functions. [PDF]

J Appl Crystallogr
Hermite functions are used to represent pair distribution functions from total scattering data in order to allow the effects of resolution to be taken into account.The use of Hermite functions to describe pair distribution functions (PDFs) from total scattering data was previously proposed by Krylov & Vvedenskii [J. Non‐Cryst.
Wang S, Gao M, Qin Y, Zhang S, Tan L, Dove MT.   +5 more
europepmc   +2 more sources

Computation of Hermite polynomials [PDF]

Mathematics of Computation, 1973
Projection methods are commonly used to approximate solutions of ordinary and partial differential equations. A basis of the subspace under consideration is needed to apply the projection method. This paper discusses methods of obtaining a basis for piecewise polynomial Hermite subspaces. A simple recursive procedure is derived for generating piecewise
George E. Trapp, Laurance C. Eisenhart
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Some Properties Involving q-Hermite Polynomials Arising from Differential Equations and Location of Their Zeros

Mathematics, 2021
Hermite polynomials are one of the Apell polynomials and various results were found by the researchers. Using Hermit polynomials combined with q-numbers, we derive different types of differential equations and study these equations. From these equations,
Cheon-Seoung Ryoo, Jungyoog Kang
doaj   +1 more source

On Hermite-Hermite matrix polynomials [PDF]

Mathematica Bohemica, 2008
In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class
M. S. Metwally, M. T. Mohamed, Ayman Shehata   +2 more
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Hermite equivalence of polynomials

Acta Arithmetica, 2023
Compared with the previous version we have inserted some changes and corrections suggested by the anonymous referee. This is the final version.
Bhargava, M., Evertse, J.H., Györy, K., Remete, L., Swaminathan, A.   +4 more
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Differential Equations Associated with Two Variable Degenerate Hermite Polynomials

Mathematics, 2020
In this paper, we introduce the two variable degenerate Hermite polynomials and obtain some new symmetric identities for two variable degenerate Hermite polynomials.
Kyung-Won Hwang, Cheon Seoung Ryoo
doaj   +1 more source

Truncated Hermite polynomials

Journal of Difference Equations and Applications, 2023
We consider the family of polynomials $p_{n}\left( x;z\right) ,$ orthogonal with respect to the inner product \[ \left\langle f,g\right\rangle = \int_{-z}^{z} f\left( x\right) g\left( x\right) e^{-x^{2}} \,dx. \] We show some properties about the coefficients in their 3-term recurrence relation, connections between $p_{n}\left( x;z\right) $ and $p_{n}^{
Diego Dominici, Francisco Marcellán
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On Some Relations between the Hermite Polynomials and Some Well-Known Classical Polynomials and the Hypergeometric Function.

مجلة العلوم البحتة والتطبيقية, 2020
The connection between different classes of special functions is a very important aspect in establishing new properties of the related classical functions that is they can inherit the properties of each other. Here we show how the Hermite polynomials are
Haniyah Saed Ben Hamdin
doaj   +1 more source

Some Identities Involving Two-Variable Partially Degenerate Hermite Polynomials Induced from Differential Equations and Structure of Their Roots

Mathematics, 2020
In this paper, we introduce two-variable partially degenerate Hermite polynomials and get some new symmetric identities for two-variable partially degenerate Hermite polynomials.
Kyung-Won Hwang, Cheon Seoung Ryoo
doaj   +1 more source

On squares of Hermite polynomials [PDF]

Aequationes Mathematicae, 1983
In this interesting paper, the authors have obtained a new integral representation for the squares of Hermite polynomials. It is further used to obtain the following asymptotic expansion \[ \bar e^{x^ 2}[H_ n(x)]^ 2/2^ nn!=(1/\sqrt{2})\sum^{\infty}_{r=0}(a_ r/\Gamma (- r+)n^{r+})+ \] \[ +((-1)^ n/\sqrt{2})\sum^{\infty}_{r=0}b_ r(x\sqrt{2/n})^{r+}J_{-p-}
Glasser, M.L., Shawagfeh, Nabil
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