In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...

polynomials, elliptic functions, and algebra. Hermite polynomials, Hermite interpolation, Hermite normal form, Hermitian operators, and cubic Hermite...

analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is...

analysis, a Hermite spline is a spline curve where each polynomial of the spline is in Hermite form. Cubic Hermite spline Hermite polynomials Hermite interpolation...

orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...

discriminants Hermite normal form, a form of row-reduced matrices Hermite numbers, integers related to the Hermite polynomials Hermite polynomials, a sequence...

orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as...

In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of polynomial interpolation, which generalizes Lagrange interpolation...

"random". PCE was first introduced in 1938 by Norbert Wiener using Hermite polynomials to model stochastic processes with Gaussian random variables. It...

Gaussian weights of certain associated Laguerre polynomials and the related generalized Hermite polynomials". Math. Comp. 18 (88): 598–616. doi:10...

for Hermite polynomials, which can be recovered from it by setting the Hermite polynomials as a special case of the associated Laguerre polynomials. Substitute...

}}}x\right),\qquad n=0,1,2,\ldots .} The functions Hn are the physicists' Hermite polynomials, H n ( z ) = ( − 1 ) n   e z 2 d n d z n ( e − z 2 ) . {\displaystyle...

§ Harmonic oscillator and Hermite functions Heat kernel Hermite polynomials Parabolic cylinder functions Laguerre polynomials § Hardy–Hille formula Hardy...

of orthogonal polynomials, Bochner's theorem is a characterization theorem of certain families of orthogonal polynomials as polynomial solutions to Sturm–Liouville...

In mathematics, the continuous q-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek...

n } {\displaystyle \{x^{n}\}} are the Hermite polynomials, the Bernoulli polynomials, and the Euler polynomials. Every Appell sequence is a Sheffer sequence...

\end{aligned}}} Cm p(η, ε) are the even Ince polynomials of order p and degree m where ε is the ellipticity parameter. The Hermite-Gaussian and Laguerre-Gaussian modes...

mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of...

B_{n,k}(\mu '_{1},\ldots ,\mu '_{n-k+1}).} Hermite polynomials can be expressed in terms of Bell polynomials as He n ⁡ ( x ) = B n ( x , − 1 , 0 , … ,...

In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are...

and Laguerre polynomials as well as Chebyshev polynomials, Jacobi polynomials and Hermite polynomials. All of these actually appear in physical problems...

asymptotics for the Hermite polynomial and Laguerre polynomial. Nowadays asymptotic expansions of this kind for orthogonal polynomials are referred to as...

mathematics, the Hermite transform is an integral transform named after the mathematician Charles Hermite that uses Hermite polynomials H n ( x ) {\displaystyle...

function can be expressed in terms of the coefficients of (modified) Hermite polynomials. The distribution first appeared in the paper Applications of Mathematics...

properties given below. Every entire function of Hermite class can be expressed as the limit of a series of polynomials having no zeros in the upper half-plane...

_{n}\left(2x{\sqrt {\pi }}\right),} where Hen(x) are the "probabilist's" Hermite polynomials, defined as H e n ( x ) = ( − 1 ) n e 1 2 x 2 ( d d x ) n e − 1 2...

functions. A similar set of polynomials, based on a generating function, is the family of Euler polynomials. The Bernoulli polynomials Bn can be defined by a...

mathematics, the continuous big q-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek...

function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields...

are involutions, the sum of absolute values of coefficients of the Hermite polynomials, the number of standard Young tableaux with n cells, and the sum...