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$\sum_{n=0}^{\infty}\frac{x^{n+1}}{n+1}P_n(x)=\frac{1}{2}\ln\left(\frac{1+x}{1-x}\right)$

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#numerical-methods #interpolation #legendre-polynomials
457
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How to calculate the integral of a Legendre polynomial

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#integration #definite-integrals #legendre-polynomials #spherical-harmonics #legendre-functions
432
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Orthonormal polynomial basis of $L^2([0,1])$

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#functional-analysis #polynomials #hilbert-spaces #orthogonal-polynomials #legendre-polynomials
118
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Orthogonality of Legendre Polynomials support

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#generating-functions #orthogonality #legendre-polynomials
125
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definite integral solution for $\int^{\pi}_{\alpha} P_{n}(\cos\theta)\:P_{m}(\cos\theta)\sin\theta\:d\theta$

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#definite-integrals #legendre-polynomials #legendre-symbol
949
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Legendre Polynomials integral

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#numerical-methods #legendre-polynomials
438
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Integral of a product of Legendre polynomials

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#definite-integrals #special-functions #orthogonality #legendre-polynomials #legendre-functions
89
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Alternative orthogonality relations between associated Legendre polynomials

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#definite-integrals #special-functions #orthogonality #orthogonal-polynomials #legendre-polynomials
68
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Associated Legendre Equation truncation

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#ordinary-differential-equations #legendre-polynomials
136
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Expanding as Fourier-Legendre series

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#fourier-analysis #legendre-polynomials
336
Views

Integral of Legendre and Chebyshev polynomials.

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#integration #legendre-polynomials #chebyshev-polynomials
268
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Understanding the dimensionality of Legendre polynomials.

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#polynomials #laplacian #legendre-polynomials #spherical-harmonics
859
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How to calculate the integral of a product of a spherical Hankel function with associated Legendre polynomials

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#definite-integrals #bessel-functions #legendre-polynomials #spherical-harmonics #legendre-functions
272
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How do I expand $\frac{1}{\sqrt{ (\boldsymbol{r-r'})^2+a} }$ in legendre polynomials (spherical harmonics)?

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#real-analysis #generating-functions #legendre-polynomials #greens-function
116
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Expand square of an associated Legendre polynomial in terms of simple associated Legendre Polynomials

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#fourier-series #legendre-polynomials #legendre-functions

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