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Using Frobenius method to solve the Legendre differential equation

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#legendre-polynomials #frobenius-method
345
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Newtonian potential expansion identity

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#multivariable-calculus #taylor-expansion #alternative-proof #legendre-polynomials #potential-theory
124
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Solving 2nd order ODE with variable coefficients

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#ordinary-differential-equations #numerical-methods #numerical-optimization #legendre-polynomials #wavelets
732
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How to tell if series terminates (Legendre ODE)

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#ordinary-differential-equations #power-series #divergent-series #legendre-polynomials
1k
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Differentiate Legendre’s equation $m$ times using Leibniz' rule for differentiating products

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#ordinary-differential-equations #derivatives #legendre-polynomials
182
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Series Solution to Legendre Equation

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#sequences-and-series #ordinary-differential-equations #proof-verification #legendre-polynomials
184
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On Legendre's Polynomial

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#legendre-polynomials
190
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Legendre - orthogonality related proof

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#legendre-polynomials
486
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Why does $\int_{-1}^1 ((1-x^2)(P_m'P_n-P_n'P_m))'\,dx = 0$ for Legendre polynomials?

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#real-analysis #functional-analysis #legendre-polynomials
129
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integral of sum of function involving legendre polynomials

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#real-analysis #calculus #integration #legendre-polynomials
108
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Identity regarding coefficients of Legendre polynomials

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#polynomials #legendre-polynomials
293
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Why the zeros of the orthogonal polynomials are symmetric about the origin if the weight function is even?

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#legendre-polynomials
610
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Orthogonality of the First Four Legendre Polynomials

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#integration #orthogonality #legendre-polynomials
650
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Domain limitations on generating function for Legendre polynomials

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#sequences-and-series #generating-functions #binomial-theorem #legendre-polynomials #negative-binomial
134
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How to derive closed form expression for the zeros of Legendre's Polynomials (Gaussian-Quadrature formulas)?

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#integration #numerical-methods #legendre-polynomials

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