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

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...

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

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...

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

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

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

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

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

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

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

}}}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...

mathematics, Hermite numbers are values of Hermite polynomials at zero argument. Typically they are defined for physicists' Hermite polynomials. The numbers...

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

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 , … ,...

\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...

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

values of a, these (that is, U and V) can be re-expressed in terms of Hermite polynomials; alternatively, they can also be expressed in terms of Bessel functions...

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

Laguerre polynomials Chebyshev polynomials Legendre polynomials Jacobi polynomials Others come from statistics: Hermite polynomials Many are studied in algebra...

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

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...

_{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...

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

the discrete q-Hermite polynomials are two closely related families hn(x;q) and ĥn(x;q) of basic hypergeometric orthogonal polynomials in the basic Askey...

{\displaystyle B(x)=1} and A ( x ) = − x {\displaystyle A(x)=-x} (Hermite polynomials) so that w ( x ) = exp ⁡ ( − x 2 2 ) {\displaystyle w(x)=\exp \left(-{\frac...