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Hermite Polynomials
"... The Hermite polynomials are defined by: Hn y ( ) ≡ −1 ()n ey 2 dn dyn e−y2 ( ) , for n ≥ 0. (1) The first six Hermite polynomials are given in the Table below: H0 y ( ) = 1321 1 2 3 ..."
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The Hermite polynomials are defined by: Hn y ( ) ≡ −1 ()n ey 2 dn dyn e−y2 ( ) , for n ≥ 0. (1) The first six Hermite polynomials are given in the Table below: H0 y ( ) = 1321 1 2 3
Hermite polynomials
, 2006
"... An explicit formula relating the probability density function with its cumulants is derived and discussed. A generalization of the GramCharlier expansion is presented, allowing to express one PDF in terms of another. The coefficients of this general expansion are explicitly obtained. ..."
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An explicit formula relating the probability density function with its cumulants is derived and discussed. A generalization of the GramCharlier expansion is presented, allowing to express one PDF in terms of another. The coefficients of this general expansion are explicitly obtained.
SPRINGS OF THE HERMITE POLYNOMIALS
, 1988
"... The Hermite polynomials, Legendre polynomials, Laguerre polynomials, Gegenbauer polynomials, and Jacobi polynomials belong to the system of classical orthogonal polynomials (see, e.g., [4]). For each class of these polynomials, ..."
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The Hermite polynomials, Legendre polynomials, Laguerre polynomials, Gegenbauer polynomials, and Jacobi polynomials belong to the system of classical orthogonal polynomials (see, e.g., [4]). For each class of these polynomials,
Asymptotics of Integrals of Hermite Polynomials
"... Integrals involving products of Hermite polynomials with the weight factor exp (−x2) over the interval (−∞, ∞) are considered. A result of Azor, Gillis and Victor (SIAM J. Math. Anal. 13 (1982) 879–890] is derived by analytic arguments and extended to higher order products. An asymptotic expansion i ..."
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Integrals involving products of Hermite polynomials with the weight factor exp (−x2) over the interval (−∞, ∞) are considered. A result of Azor, Gillis and Victor (SIAM J. Math. Anal. 13 (1982) 879–890] is derived by analytic arguments and extended to higher order products. An asymptotic expansion
GENERALIZED HERMITE POLYNOMIALS 1
, 2001
"... The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these polynomials satisfy the differential equation of the second or ..."
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The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these polynomials satisfy the differential equation of the second
A Generalization of Hermite Polynomials
"... Copyright © 2013 G. M. Habibullah and Abdul Shakoor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The intended objective of this p ..."
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of this paper is to extend the Hermite polynomials based on hypergeometric functions and to prove basic properties of the extended Hermite polynomials.
NEW BOUNDS ON THE HERMITE POLYNOMIALS
, 2004
"... Abstract. We shall establish twoside explicit inequalities, which are asymptotically sharp up to a constant factor, on the maximum value of Hk(x)e −x2 /2, on the real axis, where Hk are the Hermite polynomials. 1. ..."
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Abstract. We shall establish twoside explicit inequalities, which are asymptotically sharp up to a constant factor, on the maximum value of Hk(x)e −x2 /2, on the real axis, where Hk are the Hermite polynomials. 1.
The combinatorics of associated Hermite polynomials
, 2007
"... Abstract. We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a signreversing involution. We find combinatorial interpretations of the moments as complete matchings, connected complete matchings, oscillating tableaux, and root ..."
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Cited by 5 (0 self)
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Abstract. We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a signreversing involution. We find combinatorial interpretations of the moments as complete matchings, connected complete matchings, oscillating tableaux
Hermite polynomials on the plane
, 2007
"... The space Pn of bivariate generalised Hermite polynomials of degree n is invariant under rotations. We exploit this symmetry to construct an orthonormal basis for Pn which ℓπ consists of the rotations of a single polynomial through the angles n+1, ℓ = 0,... n. Thus we obtain an orthogonal expansion ..."
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The space Pn of bivariate generalised Hermite polynomials of degree n is invariant under rotations. We exploit this symmetry to construct an orthonormal basis for Pn which ℓπ consists of the rotations of a single polynomial through the angles n+1, ℓ = 0,... n. Thus we obtain an orthogonal expansion
A Generalization of Hermite Polynomials
"... access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we introduce a simple set ()pnH x , which is a generalized form of Hermite polynomia ..."
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access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we introduce a simple set ()pnH x , which is a generalized form of Hermite
Results 1  10
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24,534