We can use the Frobenius method for an ODE like $$u'' + qu = 0$$ where the coefficients are functions if $q$ has a particular negative power series expansion. This is when we take infinity as a regular singular point. In this case, if the indicial equation gives us roots that integer difference, how do we write the solutions? In the case where we expand around 0, we have a term including $\ln(x)$ -- what happens in the infinity case?
Frobenius method; expansion at infinity, what happens when difference of roots of indicial equation is integer?
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ordinary-differential-equations