Legendre differential equation
= Legendre differential equation
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= Legendre's differential equation
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{synonym}
The equation $(1-x^2)y\prime\prime-2xy\prime+\ell(\ell+1)y=0$ has polynomial solutions for nonnegative integer $\ell$.
The equation $(1-x^2)y\prime\prime-2xy\prime+\ell(\ell+1)y=0$ has the <Legendre polynomial> of degree $\ell$ as its normalized regular polynomial solution when $\ell$ is a nonnegative integer.