List questions from legendre-polynomials

Published on 22 Oct 2021 - 22:02

387

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Show that the inner product of the Legendre polynomials and $p\in L^2 ([-1,1])$ is equal to zero if the polynomial has degrees less than $n$

Published on 24 Oct 2021 - 19:10

136

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Integral of Associated Legendre Functions

Published on 24 Oct 2021 - 23:30

302

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Weighting for Gauss-Legendre Quadrature

Published on 25 Mar 2026 - 19:10

58

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Exact value of an infinite sum expressed in terms of a product of definite integrals involving Legendre polynomials.

Published on 10 Nov 2021 - 14:52

228

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How to relate $\int_{-1}^{1}e^{ikru} P_{\ell}(u)du$ to $j_\ell(kr)$ in a simple way?

Published on 25 Nov 2021 - 2:13

392

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Proof the Recurrence formula with Rodrigues' Formula

Published on 27 Nov 2021 - 15:27

119

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Solid angle integral, with legendre polynomials

Published on 13 Mar 2026 - 16:31

482

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Problem with Legendre-Fourier series for sinx when the number of terms approaches infinity

Published on 29 Dec 2021 - 6:13

134

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There is no continuous function $f$ so that $\int_a^b f(x)x^n dx$, $0\leq a<b$ is positive for all even $n$ and negative for odd $n$

Published on 05 Jan 2022 - 14:31

50

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Prove for general form of function at -x containing derivatives of order n

Published on 25 Mar 2026 - 22:26

167

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Convert ODE to a form of Bessel differential equation

Published on 18 Jan 2022 - 1:32

30

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Which of the following series converge? (With Legendre-Polynomials)

Published on 25 Jan 2022 - 11:35

220

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Closed form expression for series involving Legendre polynomials

Published on 25 Jan 2022 - 13:41

172

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The values of $P_n(x)$ at the zeros of $P'_n(x)$

Published on 25 Jan 2022 - 18:42

List Question

Initial guess in Newton-Raphson method.

Show that the inner product of the Legendre polynomials and $p\in L^2 ([-1,1])$ is equal to zero if the polynomial has degrees less than $n$

Integral of Associated Legendre Functions

Weighting for Gauss-Legendre Quadrature

Exact value of an infinite sum expressed in terms of a product of definite integrals involving Legendre polynomials.

How to relate $\int_{-1}^{1}e^{ikru} P_{\ell}(u)du$ to $j_\ell(kr)$ in a simple way?

Proof the Recurrence formula with Rodrigues' Formula

Solid angle integral, with legendre polynomials

Problem with Legendre-Fourier series for sinx when the number of terms approaches infinity

There is no continuous function $f$ so that $\int_a^b f(x)x^n dx$, $0\leq a<b$ is positive for all even $n$ and negative for odd $n$

Prove for general form of function at -x containing derivatives of order n

Convert ODE to a form of Bessel differential equation

Which of the following series converge? (With Legendre-Polynomials)

Closed form expression for series involving Legendre polynomials

The values of $P_n(x)$ at the zeros of $P'_n(x)$

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