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f''+(E-A(A+1)/x^2)f=0, where A is a positive integer, E is a real constant

the domain is [0, \infty).

the boundary condition is f(x=0)=0

since this is a linear equation, i only need to determine f up to a overall constant

how to do this numerically from the origin and outward?

we can prove that in the neighborhood of the origin, f is on the order of x^(A+1)