List questions from legendre-polynomials

Published on 01 Apr 2019 - 15:13

234

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Prove that the Legendre polynomial holds true using the generating function and a binomial expansion.

Published on 02 Apr 2019 - 0:49

611

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Trying to prove that $\pi$ is irrational using Legendre Polynomials.

Published on 14 Apr 2019 - 17:15

37

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Proof for a Legendre polynomial identity on a 2-sphere that appears in cosmology

Published on 25 Apr 2019 - 13:04

790

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$L^2$ norm of the first derivative of Legendre polynomials

Published on 25 Mar 2026 - 3:21

138

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Expressing spherical functions with zonal harmonics

Published on 08 May 2019 - 1:28

232

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Recurrence relations and power series solution

Published on 27 May 2019 - 14:46

74

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Numerically approximating functions on the sphere by rotating zonal harmonics.

Published on 30 May 2019 - 21:48

226

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Integral Expression of Legendre Polynomials

Published on 02 Jun 2019 - 0:16

83

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Differing Forms of Legendre Polynomials

Published on 06 Jun 2019 - 18:21

137

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How to convert a hypergeom function to the Legendre function?

Published on 23 Feb 2026 - 13:23

960

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Integral with Legendre Polynomial $\int x^2(P_l(x))^2dx$

Published on 12 Jun 2019 - 19:58

485

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Rodrigues' formula proof

Published on 14 Jun 2019 - 16:26

565

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Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

Published on 19 Jun 2019 - 4:48

131

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$\left|\frac{d^n}{dx^n}(x^2-1)^n\right|\le\sqrt\frac2\pi\cdot\frac{2^nn!}{\sqrt n}\cdot\frac1{\sqrt[4]{1-x^2}}$, a bound for Legendre Polynomial

Published on 29 Jun 2019 - 12:17

List Question

Orthogonal Property of Legendre Polynomials

Prove that the Legendre polynomial holds true using the generating function and a binomial expansion.

Trying to prove that $\pi$ is irrational using Legendre Polynomials.

Proof for a Legendre polynomial identity on a 2-sphere that appears in cosmology

$L^2$ norm of the first derivative of Legendre polynomials

Expressing spherical functions with zonal harmonics

Recurrence relations and power series solution

Numerically approximating functions on the sphere by rotating zonal harmonics.

Integral Expression of Legendre Polynomials

Differing Forms of Legendre Polynomials

How to convert a hypergeom function to the Legendre function?

Integral with Legendre Polynomial $\int x^2(P_l(x))^2dx$

Rodrigues' formula proof

Evaluate $\int_0^1 x^{a-1}(1-x)^{b-1}\operatorname{Li}_3(x) \, dx$

$\left|\frac{d^n}{dx^n}(x^2-1)^n\right|\le\sqrt\frac2\pi\cdot\frac{2^nn!}{\sqrt n}\cdot\frac1{\sqrt[4]{1-x^2}}$, a bound for Legendre Polynomial

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