List questions from hermite-polynomials

Published on 16 Sep 2019 - 16:45

63

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Can a generalization of the Hermite function-like "basis" $φ_n(x) = D^n \exp(-x^2/2)$ be orthonormal in $L^2$?

Published on 17 Sep 2019 - 12:12

35

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Can $\frac{d^k}{dx^k} e^{\frac{x^2}{2}}$ be written in terms of Hermite polynomials?

Published on 23 Sep 2019 - 14:35

430

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Approximation to the $n$-th derivative using reproducing kernels.

Published on 22 Mar 2026 - 10:48

108

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The expectation of a hermitian matrix quadratic form $E\left[ \mathbf{XF}{{\mathbf{F}}^{H}}{{\mathbf{X}}^{H}} \right]$

Published on 21 Nov 2019 - 13:39

138

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Evaluating $\int_{-\infty}^{\infty} e^{-x^2 / 2} H_n(x) \space dx$

Published on 02 Dec 2019 - 0:40

223

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Derivatives of exponential and Hermite polynomials

Published on 10 Dec 2019 - 9:46

327

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Hermite polynomials as a basis for generating function

Published on 15 Jan 2020 - 11:48

254

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Hermite interpolation and basis functions.

Published on 28 Jan 2020 - 13:08

92

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The integral with two Hermite polynomials

Published on 04 Feb 2020 - 21:15

110

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A contradiction? Inconsistent expression of Hermite functions as eigenvalues of Fourier transform.

Published on 24 Mar 2026 - 21:01

191

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Notes on Hermite Polynomials

Published on 09 Feb 2020 - 9:39

98

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combinatorial formula for Hermite polynomials

Published on 19 Feb 2020 - 22:19

746

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Fourier transform of a product of the Hermite polynomials

Published on 18 Mar 2020 - 15:07

735

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Fourier Transform of Hermite polynomial $H_n(x)e^{-\frac{x^2}{2}}$

Published on 23 Mar 2020 - 20:53

List Question

Function series involving Hermite Polynomials

Can a generalization of the Hermite function-like "basis" $φ_n(x) = D^n \exp(-x^2/2)$ be orthonormal in $L^2$?

Can $\frac{d^k}{dx^k} e^{\frac{x^2}{2}}$ be written in terms of Hermite polynomials?

Approximation to the $n$-th derivative using reproducing kernels.

The expectation of a hermitian matrix quadratic form $E\left[ \mathbf{XF}{{\mathbf{F}}^{H}}{{\mathbf{X}}^{H}} \right]$

Evaluating $\int_{-\infty}^{\infty} e^{-x^2 / 2} H_n(x) \space dx$

Derivatives of exponential and Hermite polynomials

Hermite polynomials as a basis for generating function

Hermite interpolation and basis functions.

The integral with two Hermite polynomials

A contradiction? Inconsistent expression of Hermite functions as eigenvalues of Fourier transform.

Notes on Hermite Polynomials

combinatorial formula for Hermite polynomials

Fourier transform of a product of the Hermite polynomials

Fourier Transform of Hermite polynomial $H_n(x)e^{-\frac{x^2}{2}}$

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