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...

generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor...

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

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...

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

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...

formula. The partial or incomplete exponential Bell polynomials are a triangular array of polynomials given by B n , k ( x 1 , x 2 , … , x n − k + 1 ) =...

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...

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

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

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

quadrature Legendre polynomials Spherical harmonics Whipple's transformation of Legendre functions Laguerre polynomials Hermite polynomials Courant & Hilbert...

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

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

The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)} and...

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

the formulas for Legendre, Laguerre and Hermite polynomials: Rodrigues stated his formula for Legendre polynomials P n {\displaystyle P_{n}} : P n ( x )...

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

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

\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, 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 Mehler...

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...

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

spherical harmonics play a similar role in higher dimensions to the Hermite polynomials in dimension one. Specifically, if f(x) = e−π|x|2P(x) for some P(x)...

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