Question

what is legendr's equation?
what is bessel"s equation?

Answer 1

They are ordinary differential equations that are solved using Frobenius' Method (series solution).

Legenre's equation:\[(1-x^2)\frac{d^2y}{dx^2}-2x \frac{dy}{dx}+l(l+1)y=0\]Bessel's equation:\[x^2\frac{d^2y}{dx^2}+x \frac{dy}{dx}+(x^2-{\nu}^2)y=0\]These equations are important in mathematical physics.