Question

Calculate $ \int_{-\infty}^{\infty} x^4 H(x)^2 e^{-x^2} dx$ where $H(x)$ is a Hermite polynomial

score 287 · Answer 1 · 2013-09-07 05:57:19

287

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Calculate $ \int_{-\infty}^{\infty} x^4 H(x)^2 e^{-x^2} dx$ where $H(x)$ is a Hermite polynomial

Published on 07 Sep 2013 - 5:57

score 5.8k · Answer 2 · 2013-10-03 13:46:42

5.8k

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Is each Chebyshev Polynomial orthogonal with respect to the weight function?

Published on 03 Oct 2013 - 13:46

score 136 · Answer 3 · 2013-10-08 01:28:52

136

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Linear Algebra Orthogonality: Finding orthogonal basis

Published on 08 Oct 2013 - 1:28

score 869 · Answer 4 · 2013-10-08 15:54:59

869

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Explicit Formula for the Integral of the Legendre Polynomial

Published on 08 Oct 2013 - 15:54

score 401 · Answer 5 · 2013-10-14 10:54:12

401

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Determinant of a circulant matrix as Chebyshev-like recurrence

Published on 14 Oct 2013 - 10:54

score 13.6k · Answer 6 · 2013-10-15 13:53:50

13.6k

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Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros

Published on 15 Oct 2013 - 13:53

score 594 · Answer 7 · 2013-10-18 07:02:47

594

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Recurrence relation and orthogonal monic polynomials

Published on 18 Oct 2013 - 7:02

score 9.9k · Answer 8 · 2026-03-26 11:06:11

9.9k

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Calculation of Chebyshev coefficients

Published on 26 Mar 2026 - 11:06

score 764 · Answer 9 · 2013-10-22 01:44:56

764

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Transfrom a Legendre polynomial from $\int_{-1}^{1}\phi_j(x)\phi_k(x)dx $ into $\int_{a}^{b}\phi_j(t)\phi_k(t)dt$ given $t=\dfrac{1}{2}[(b-a)x+(a+b)]$

Published on 22 Oct 2013 - 1:44

score 2.5k · Answer 10 · 2026-03-26 11:04:23

2.5k

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Prove $T_n(x)$ of Chebyshev Polynomial given the recurrence relation

Published on 26 Mar 2026 - 11:04

score 403 · Answer 11 · 2013-10-24 20:46:27

403

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Linear Algebra Projections and orthogonality

Published on 24 Oct 2013 - 20:46

score 2.9k · Answer 12 · 2013-10-26 07:27:47

2.9k

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Proof of A is orthogonal $\Leftrightarrow \|Ax\|=\|x\|$

Published on 26 Oct 2013 - 7:27

score 274 · Answer 13 · 2013-10-26 21:46:54

274

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Wick polynomials - hard time following the basics...

Published on 26 Oct 2013 - 21:46

score 952 · Answer 14 · 2013-10-29 21:57:58

952

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Recurrence relation for Jacobi polynomials with negative parameter $\beta$

Published on 29 Oct 2013 - 21:57

score 946 · Answer 15 · 2013-10-31 15:57:53

946

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Orthogonal Matrix statements/proofs

Published on 31 Oct 2013 - 15:57

List Question

Calculate $ \int_{-\infty}^{\infty} x^4 H(x)^2 e^{-x^2} dx$ where $H(x)$ is a Hermite polynomial

Is each Chebyshev Polynomial orthogonal with respect to the weight function?

Linear Algebra Orthogonality: Finding orthogonal basis

Explicit Formula for the Integral of the Legendre Polynomial

Determinant of a circulant matrix as Chebyshev-like recurrence

Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros

Recurrence relation and orthogonal monic polynomials

Calculation of Chebyshev coefficients

Transfrom a Legendre polynomial from $\int_{-1}^{1}\phi_j(x)\phi_k(x)dx $ into $\int_{a}^{b}\phi_j(t)\phi_k(t)dt$ given $t=\dfrac{1}{2}[(b-a)x+(a+b)]$

Prove $T_n(x)$ of Chebyshev Polynomial given the recurrence relation

Linear Algebra Projections and orthogonality

Proof of A is orthogonal $\Leftrightarrow \|Ax\|=\|x\|$

Wick polynomials - hard time following the basics...

Recurrence relation for Jacobi polynomials with negative parameter $\beta$

Orthogonal Matrix statements/proofs

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