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Problems regarding integrals involving Legendre polynomials: $\int_{-1}^1 x^2 P_{n-1}(x)P_{n+1}(x)dx = \frac{2n(n+1)}{(2n-1)(2n+1)(2n+3)}$

score 2.6k · Answer 1 · 2012-10-02 11:03:03

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Problems regarding integrals involving Legendre polynomials: $\int_{-1}^1 x^2 P_{n-1}(x)P_{n+1}(x)dx = \frac{2n(n+1)}{(2n-1)(2n+1)(2n+3)}$

Published on 02 Oct 2012 - 11:03

score 1.9k · Answer 2 · 2012-10-21 17:42:35

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Finding the zeroes using Chebyshev polynomials

Published on 21 Oct 2012 - 17:42

score 598 · Answer 3 · 2012-11-02 11:55:34

598

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A quantitative version of the Weierstrass' Approximation Theorem

Published on 02 Nov 2012 - 11:55

score 4.2k · Answer 4 · 2012-11-04 14:18:22

4.2k

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Showing Hermite polynomials are orthogonal

Published on 04 Nov 2012 - 14:18

score 470 · Answer 5 · 2012-11-05 19:34:34

470

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Constructing second degree Legendre Polynomials

Published on 05 Nov 2012 - 19:34

score 1.3k · Answer 6 · 2012-11-13 10:57:23

1.3k

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Colleague Matrix

Published on 13 Nov 2012 - 10:57

score 1k · Answer 7 · 2012-11-14 16:49:13

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Zernike and Legendre polynomials

Published on 14 Nov 2012 - 16:49

score 4.4k · Answer 8 · 2012-12-21 00:27:01

4.4k

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Legendre Polynomials Triple Product

Published on 21 Dec 2012 - 0:27

score 1.4k · Answer 9 · 2013-01-04 09:50:28

1.4k

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How to find a set of polynomials that are orthonormal with respect to this inner product?

Published on 04 Jan 2013 - 9:50

score 1.9k · Answer 10 · 2013-01-15 21:55:11

1.9k

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How to work out orthogonal polynomials for regression model

Published on 15 Jan 2013 - 21:55

score 4.4k · Answer 11 · 2013-01-17 19:38:11

4.4k

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Integral of Hermite polynomial multiplied by $\exp(-x^2/2)$

Published on 17 Jan 2013 - 19:38

score 2.8k · Answer 12 · 2013-01-20 21:12:43

2.8k

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Published on 20 Jan 2013 - 21:12

score 312 · Answer 13 · 2013-01-29 17:29:25

312

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Published on 29 Jan 2013 - 17:29

score 2.6k · Answer 14 · 2013-02-10 21:05:05

2.6k

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Calculate an integral involving Hermite polynomials

Published on 10 Feb 2013 - 21:05

score 4.1k · Answer 15 · 2026-03-25 16:14:02

4.1k

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Use of a substitution to prove that $e^{2xt-t^2}$ is the exponential generating function of the Hermite polynomials

Published on 25 Mar 2026 - 16:14

List Question

Problems regarding integrals involving Legendre polynomials: $\int_{-1}^1 x^2 P_{n-1}(x)P_{n+1}(x)dx = \frac{2n(n+1)}{(2n-1)(2n+1)(2n+3)}$

Finding the zeroes using Chebyshev polynomials

A quantitative version of the Weierstrass' Approximation Theorem

Showing Hermite polynomials are orthogonal

Constructing second degree Legendre Polynomials

Colleague Matrix

Zernike and Legendre polynomials

Legendre Polynomials Triple Product

How to find a set of polynomials that are orthonormal with respect to this inner product?

How to work out orthogonal polynomials for regression model

Integral of Hermite polynomial multiplied by $\exp(-x^2/2)$

Legendre polynomials, Laguerre polynomials: Basic concept

How to find asymptotic behaviour?

Calculate an integral involving Hermite polynomials

Use of a substitution to prove that $e^{2xt-t^2}$ is the exponential generating function of the Hermite polynomials

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