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Deriving normalization for the shifted associated Legendre function

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#orthogonality #legendre-polynomials #legendre-functions
321
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Coefficient of the Highest Degree in the Power Series Solution to Legendre's Differential Equation

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#linear-algebra #power-series #legendre-polynomials
157
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Question on the method of Gauss-Legendre

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#numerical-methods #numerical-linear-algebra #legendre-polynomials #runge-kutta-methods
150
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Prove $1+\sum_{k=1}^{p} \frac{(-1)^k.n(n-1)(n-2)\cdots(n-2k+1)}{2^k.k!.(2n-1)(2n-3)\cdots(2n-2k+1)}=\frac{2^n(n!)^2}{(2n)!}$

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#sequences-and-series #legendre-polynomials #legendre-functions
69
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Integral form of legendre polynomial of second kind

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#legendre-polynomials
434
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The coefficient and asymptotic in generating function

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#combinatorics #asymptotics #generating-functions #analyticity #legendre-polynomials
164
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Spherical Harmonics Sum Identity

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#summation #physics #mathematical-physics #legendre-polynomials #spherical-harmonics
75
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Behavior of Legendre polynomials $P_\ell(\cos\theta)$ under $\theta\to\pi-\theta$

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#calculus #derivatives #legendre-polynomials
107
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Integral of Legendre polynomials with tangent

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#integration #boundary-value-problem #legendre-polynomials
133
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Expand Associated Legendre Polynomials in the basis of shifted Associated Legendre Polynomials

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#definite-integrals #orthogonal-polynomials #legendre-polynomials
171
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Shifted Legendre polynomials symmetry relation

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#real-analysis #hilbert-spaces #legendre-polynomials
159
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How to simplify a partial sum obtained by Legendre polynomials

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#summation #fourier-analysis #binomial-coefficients #legendre-polynomials
115
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Alternative definition of Legendre polynomials

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#recurrence-relations #definition #special-functions #legendre-polynomials
46
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Formula for the derivative of finite power series in reversed order of terms.

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#ordinary-differential-equations #derivatives #power-series #legendre-polynomials
76
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Legendre Polynomial Identity

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#legendre-polynomials

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