Differential equations can often be solved by the method of Fourier transform. I have a particular equation in mind that appears very often in physical applications which is the Legendre differential equation: $$(1-x^2)y^{\prime\prime}-2xy^{\prime}+l(l+1)y=0.$$ I know that this can be solved by the method of series solution. But does the Fourier transform trick work here? If not why?
2026-03-25 14:21:11.1774448471
Fourier transform trick in solving Legendre's differential equation
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