Legendre Equation
Tags: #math #legendre equationEquation
$$(1x^{2})\frac{\mathrm{d}^{2} y}{\mathrm{d} x^{2}}2x\frac{\mathrm{d} y}{\mathrm{d} x}+l(l+1)y=0 \\ P_{l}(x)=\frac{1}{2^{l}l!}(\frac{\mathrm{d}}{\mathrm{d} x})^{l}(x^21)^{l}\\ P_{l}(x)=\frac{1}{l}[(2l1)xP_{l1}(x)(l1)P_{l2}(x)]$$Latex Code
(1x^{2})\frac{\mathrm{d}^{2} y}{\mathrm{d} x^{2}}2x\frac{\mathrm{d} y}{\mathrm{d} x}+l(l+1)y=0 \\ P_{l}(x)=\frac{1}{2^{l}l!}(\frac{\mathrm{d}}{\mathrm{d} x})^{l}(x^21)^{l}\\ P_{l}(x)=\frac{1}{l}[(2l1)xP_{l1}(x)(l1)P_{l2}(x)]
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Introduction
Explanation
 Solutions of Legendre equations are Legendre polynomials
 Recursion relation:
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