Question

Formal solution of $ -[(1-x^2)y']' = \mu y + f(x)$

score 65 · Answer 1 · 2018-07-11 21:09:15

65

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Formal solution of $ -[(1-x^2)y']' = \mu y + f(x)$

Published on 11 Jul 2018 - 21:09

score 626 · Answer 2 · 2026-02-23 13:25:40

626

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Sum of associated Legendre functions

Published on 23 Feb 2026 - 13:25

score 127 · Answer 3 · 2018-08-05 06:41:55

127

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Upper bound of the integral $\frac{a^{n}}{n!}\int_{0}^{1} e^{at} t^{n}(1-t)^{n}dt$.

Published on 05 Aug 2018 - 6:41

score 627 · Answer 4 · 2018-08-14 21:42:39

627

Views

Showing that the first two Legendre polynomials, $P_0(x) = 1$ and $P_1(x) = x$ are orthogonal for $x \in [−1,1]$

Published on 14 Aug 2018 - 21:42

score 223 · Answer 5 · 2026-03-24 22:10:53

223

Views

Determining Rodriguez formula for Legendre polynomials

Published on 24 Mar 2026 - 22:10

score 944 · Answer 6 · 2018-08-26 15:59:42

944

Views

Spherical harmonics and Dirac delta integrals

Published on 26 Aug 2018 - 15:59

score 1.7k · Answer 7 · 2026-02-22 21:39:46

1.7k

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Roots of the Indicial Polynomial of the Legendre equation $(1-z^2)u''-2zu'+v(v+1)u=0$

Published on 22 Feb 2026 - 21:39

score 103 · Answer 8 · 2026-03-24 22:16:05

103

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I want to prove that $ \int_{-1}^{+1}xp_{s}(x)p_{r}(x)dx=\delta_{r,s+1}\frac{2r}{(2r+1)(2r-1)}+\delta_{s,r+1}\frac{2s}{(2s+1)(2s-1)}. $

Published on 24 Mar 2026 - 22:16

score 115 · Answer 9 · 2026-03-23 10:56:26

115

Views

Confused about Arccosecant and Legendre & Pochhammer Notations

Published on 23 Mar 2026 - 10:56

score 162 · Answer 10 · 2018-09-11 16:23:23

162

Views

The Distribution of Abscissae and Sums of Weights in Gaussian Quadrature

Published on 11 Sep 2018 - 16:23

score 374 · Answer 11 · 2026-03-22 15:31:14

374

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Since the solution of the Legendre’s equations are the Legendre polynomials $P_n(\mu)$, write the general solution for $u(r, \theta)$.

Published on 22 Mar 2026 - 15:31

score 533 · Answer 12 · 2018-09-21 04:29:12

533

Views

Integration of Legendre Polynomials with Dirac Delta function

Published on 21 Sep 2018 - 4:29

score 243 · Answer 13 · 2018-10-02 13:15:36

243

Views

Fourier-Legendre Series and Closure

Published on 02 Oct 2018 - 13:15

score 163 · Answer 14 · 2018-10-04 14:56:24

163

Views

Finding $a>1$ such that $\int_0^\pi \tfrac{\sin x\,\mathrm{d}x} { \sqrt{1 − 2a\cos x + a^2}}$ equals given constant

Published on 04 Oct 2018 - 14:56

score 99 · Answer 15 · 2018-10-04 17:01:30

99

Views

Motivation for the smart guess of Legendre's Associated Polynomial

Published on 04 Oct 2018 - 17:01

List Question

Formal solution of $ -[(1-x^2)y']' = \mu y + f(x)$

Sum of associated Legendre functions

Upper bound of the integral $\frac{a^{n}}{n!}\int_{0}^{1} e^{at} t^{n}(1-t)^{n}dt$.

Showing that the first two Legendre polynomials, $P_0(x) = 1$ and $P_1(x) = x$ are orthogonal for $x \in [−1,1]$

Determining Rodriguez formula for Legendre polynomials

Spherical harmonics and Dirac delta integrals

Roots of the Indicial Polynomial of the Legendre equation $(1-z^2)u''-2zu'+v(v+1)u=0$

I want to prove that $ \int_{-1}^{+1}xp_{s}(x)p_{r}(x)dx=\delta_{r,s+1}\frac{2r}{(2r+1)(2r-1)}+\delta_{s,r+1}\frac{2s}{(2s+1)(2s-1)}. $

Confused about Arccosecant and Legendre & Pochhammer Notations

The Distribution of Abscissae and Sums of Weights in Gaussian Quadrature

Since the solution of the Legendre’s equations are the Legendre polynomials $P_n(\mu)$, write the general solution for $u(r, \theta)$.

Integration of Legendre Polynomials with Dirac Delta function

Fourier-Legendre Series and Closure

Finding $a>1$ such that $\int_0^\pi \tfrac{\sin x\,\mathrm{d}x} { \sqrt{1 − 2a\cos x + a^2}}$ equals given constant

Motivation for the smart guess of Legendre's Associated Polynomial

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