Question

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

score 68 · Answer 1 · 2026-04-14 19:37:55

68

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

Published on 14 Apr 2026 - 19:37

score 630 · Answer 2 · 2026-04-24 11:20:09

630

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Sum of associated Legendre functions

Published on 24 Apr 2026 - 11:20

score 131 · Answer 3 · 2026-05-10 16:35:50

131

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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 10 May 2026 - 16:35

score 630 · Answer 4 · 2026-04-16 01:57:56

630

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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 16 Apr 2026 - 1:57

score 224 · Answer 5 · 2026-05-10 15:58:41

224

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Determining Rodriguez formula for Legendre polynomials

Published on 10 May 2026 - 15:58

score 950 · Answer 6 · 2026-05-10 15:50:05

950

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Spherical harmonics and Dirac delta integrals

Published on 10 May 2026 - 15:50

score 1.7k · Answer 7 · 2026-04-16 01:43:31

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 16 Apr 2026 - 1:43

score 104 · Answer 8 · 2026-05-10 16:13:29

104

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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 10 May 2026 - 16:13

score 121 · Answer 9 · 2026-04-29 12:16:19

121

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Confused about Arccosecant and Legendre & Pochhammer Notations

Published on 29 Apr 2026 - 12:16

score 164 · Answer 10 · 2026-05-10 18:30:43

164

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The Distribution of Abscissae and Sums of Weights in Gaussian Quadrature

Published on 10 May 2026 - 18:30

score 375 · Answer 11 · 2026-03-25 01:38:28

375

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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 25 Mar 2026 - 1:38

score 536 · Answer 12 · 2026-04-09 09:54:13

536

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Integration of Legendre Polynomials with Dirac Delta function

Published on 09 Apr 2026 - 9:54

score 247 · Answer 13 · 2026-04-10 16:03:05

247

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Fourier-Legendre Series and Closure

Published on 10 Apr 2026 - 16:03

score 166 · Answer 14 · 2026-04-16 10:55:28

166

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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 16 Apr 2026 - 10:55

score 102 · Answer 15 · 2026-04-14 16:48:22

102

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Motivation for the smart guess of Legendre's Associated Polynomial

Published on 14 Apr 2026 - 16:48

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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