Question

Is it common to generate complex roots to the indicial equation with the frobenius method of solving DEs by power series?

Answer 1

for example, the DE i have been toying around with is x^2y'' + (x+x^2)y' + y' = 0. a sort of variation on the stock cauchy-euler x^2y'' + xy' +y = 0 equation. the problem is finding the solution as the sum of the real and imaginary parts of the DE. the recurrence relation is nightmarishly defined and mired in complex notation. is this common?

Answer 2

i am also aware of the similarity of the DE to your typical laguerre polynomial / hypergeometric function but i'd prefer discussion related to power series solution is possible ... !