In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...
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polynomials, elliptic functions, and algebra. Hermite polynomials, Hermite interpolation, Hermite normal form, Hermitian operators, and cubic Hermite...
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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...
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generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor...
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orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as...
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discriminants Hermite normal form, a form of row-reduced matrices Hermite numbers, integers related to the Hermite polynomials Hermite polynomials, a sequence...
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orthogonal polynomials are the classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The...
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Gaussian weights of certain associated Laguerre polynomials and the related generalized Hermite polynomials". Math. Comp. 18 (88): 598–616. doi:10...
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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...
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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...
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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 ) =...
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mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of...
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mathematics, the Hermite transform is an integral transform named after the mathematician Charles Hermite that uses Hermite polynomials H n ( x ) {\displaystyle...
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In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of polynomial interpolation, which generalizes Lagrange interpolation...
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"random". PCE was first introduced in 1938 by Norbert Wiener using Hermite polynomials to model stochastic processes with Gaussian random variables. It...
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quadrature Legendre polynomials Spherical harmonics Whipple's transformation of Legendre functions Laguerre polynomials Hermite polynomials Courant & Hilbert...
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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...
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Spline (mathematics) (redirect from Piecewise polynomial curve)
function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields...
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Appell sequence (redirect from Appell polynomials)
n } {\displaystyle \{x^{n}\}} are the Hermite polynomials, the Bernoulli polynomials, and the Euler polynomials. Every Appell sequence is a Sheffer sequence...
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}}}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...
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Rodrigues' formula (category Orthogonal polynomials)
the formulas for Legendre, Laguerre and Hermite polynomials: Rodrigues stated his formula for Legendre polynomials P n {\displaystyle P_{n}} : P n ( x )...
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Laguerre polynomials Chebyshev polynomials Legendre polynomials Jacobi polynomials Others come from statistics: Hermite polynomials Many are studied in algebra...
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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...
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Gaussian beam (redirect from Hermite-Gaussian mode)
\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...
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mathematics, the continuous big q-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek...
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polynomials Heat polynomial — see caloric polynomial Heckman–Opdam polynomials Hermite polynomials Hurwitz polynomial Jack function Jacobi polynomials Koornwinder...
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In mathematics, the continuous q-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek...
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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)...
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Mehler kernel (redirect from Mehler's Hermite polynomial formula)
§ Harmonic oscillator and Hermite functions Heat kernel Hermite polynomials Parabolic cylinder functions Laguerre polynomials § Hardy–Hille formula Mehler...
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It is one of several graph polynomials studied in algebraic graph theory. Several different types of matching polynomials have been defined. Let G be...
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