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find $a_L$ in $ \frac{Y_{\ell}^{m}Y_{\ell'}^{-m}}{\sin^2\theta}=\sum_{L=0}^{\ell+\ell'}a_LY_L^0$

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#legendre-polynomials #spherical-harmonics #legendre-functions
193
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Trouble proving identity with Legendre polynomials

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#calculus #integration #derivatives #legendre-polynomials
813
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How to solve Legendre's differential equation without power series assumption?

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#ordinary-differential-equations #power-series #legendre-polynomials #frobenius-method
470
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Higher-order Derivatives of Legendre Polynomials at endpoints

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#orthogonal-polynomials #legendre-polynomials #chebyshev-polynomials
222
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Pointwise convergence of Fourier-Legendre Series expansion

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#real-analysis #convergence-divergence #fourier-analysis #lp-spaces #legendre-polynomials
936
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Using Orthogonality of Legendre Polynomials to determine a Recurrence Relation

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#orthogonality #legendre-polynomials
114
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Show that Legendre polynomial satisfies $\int P_n(x)dx=\frac{1}{2^{n+1}}[P_{n+1}(x)-P_{n-1}(x)]$

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#ordinary-differential-equations #proof-verification #legendre-polynomials
896
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Prove that the Legendre polynomial satisfies $\int_{-1}^1(1-x^2) P_m' P_n' dx=0$

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#ordinary-differential-equations #legendre-polynomials
484
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Prove that Legendre polynomial satisfies $\int_{-1}^1 x P_n(x) P_m '(x) dx=0$

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#ordinary-differential-equations #legendre-polynomials
335
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Integrate product of two spherical harmonics over half-sphere

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#definite-integrals #legendre-polynomials #spherical-harmonics
231
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Legendre Polynomial as an integral

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#ordinary-differential-equations #legendre-polynomials
136
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Integrals with Legendre polynomials

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#integration #legendre-polynomials
197
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Calculating Fourier expansion using Legendre Polynomials

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#integration #fourier-series #orthogonal-polynomials #legendre-polynomials
273
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Stuck on this Legendre polynomial ODE question

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#ordinary-differential-equations #legendre-polynomials
928
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Use Bonnet recursion formula to prove by induction

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#numerical-methods #induction #recurrence-relations #legendre-polynomials

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