Question

How do we determine if an operator over real functions is normal?

score 23 · Answer 1 · 2022-10-05 13:46:48

23

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How do we determine if an operator over real functions is normal?

Published on 05 Oct 2022 - 13:46

score 125 · Answer 2 · 2022-10-10 21:41:13

125

Views

Reference(book or article) for an explicit formula of Legendre polynomials

Published on 10 Oct 2022 - 21:41

score 191 · Answer 3 · 2022-10-16 20:03:33

191

Views

Integration of product of two Legendre polynomial

Published on 16 Oct 2022 - 20:03

score 65 · Answer 4 · 2022-10-17 16:24:21

65

Views

Simplification of an infinite sum consisting of Legendre polynomials

Published on 17 Oct 2022 - 16:24

score 318 · Answer 5 · 2022-10-17 18:23:04

318

Views

Deriving the integral form of the Legendre polynomials from the derivative form

Published on 17 Oct 2022 - 18:23

score 138 · Answer 6 · 2022-10-20 10:31:24

138

Views

Convergence of an integral with Legendre polynomials

Published on 20 Oct 2022 - 10:31

score 99 · Answer 7 · 2022-10-25 01:35:54

99

Views

Prove that $\int_{0}^{1} P_{l}(x)dx = \dfrac{P_{l-1} (0)}{l + 1}$

Published on 25 Oct 2022 - 1:35

score 141 · Answer 8 · 2022-10-29 04:12:27

141

Views

Prove that $\sum_{y=0}^{p-1}\left(\frac{y}{p}\right)\left(\frac{y+d}{p}\right)=-1$

Published on 29 Oct 2022 - 4:12

score 295 · Answer 9 · 2022-11-01 19:28:29

295

Views

Prove: $\int_{-1}^1 x^n P_n(x) dx = \frac{2^{n+1}n!^2}{(2n+1)!}$

Published on 01 Nov 2022 - 19:28

score 115 · Answer 10 · 2022-11-07 00:16:15

115

Views

Prove $\int_{0}^{1}x^{m}P_{l}(x)dx = \frac{m! (m - l + 1)!!}{(m - l +1)!(m + l +1)!!}$

Published on 07 Nov 2022 - 0:16

score 109 · Answer 11 · 2022-11-14 14:59:40

109

Views

Prove of a Legendre's polynomial problem

Published on 14 Nov 2022 - 14:59

score 139 · Answer 12 · 2022-11-17 22:51:52

139

Views

How to prove Legendre Polynomials' recurrence relation without using explicit formula?

Published on 17 Nov 2022 - 22:51

score 114 · Answer 13 · 2022-11-20 20:59:57

114

Views

A closed-form formula involving Legendre polynomials for the "information potential" of the binomial distribution

Published on 20 Nov 2022 - 20:59

score 88 · Answer 14 · 2022-11-22 12:28:01

88

Views

Distributional Fourier Transform of $P_{n}(\cos x)$

Published on 22 Nov 2022 - 12:28

score 73 · Answer 15 · 2022-11-22 14:06:25

73

Views

Could someone help prove some properties of Legendre Polynomials?

Published on 22 Nov 2022 - 14:06

List Question

How do we determine if an operator over real functions is normal?

Reference(book or article) for an explicit formula of Legendre polynomials

Integration of product of two Legendre polynomial

Simplification of an infinite sum consisting of Legendre polynomials

Deriving the integral form of the Legendre polynomials from the derivative form

Convergence of an integral with Legendre polynomials

Prove that $\int_{0}^{1} P_{l}(x)dx = \dfrac{P_{l-1} (0)}{l + 1}$

Prove that $\sum_{y=0}^{p-1}\left(\frac{y}{p}\right)\left(\frac{y+d}{p}\right)=-1$

Prove: $\int_{-1}^1 x^n P_n(x) dx = \frac{2^{n+1}n!^2}{(2n+1)!}$

Prove $\int_{0}^{1}x^{m}P_{l}(x)dx = \frac{m! (m - l + 1)!!}{(m - l +1)!(m + l +1)!!}$

Prove of a Legendre's polynomial problem

How to prove Legendre Polynomials' recurrence relation without using explicit formula?

A closed-form formula involving Legendre polynomials for the "information potential" of the binomial distribution

Distributional Fourier Transform of $P_{n}(\cos x)$

Could someone help prove some properties of Legendre Polynomials?

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