Are these analytic? (easy stuff)

[t_n_p]

Homework Statement

I have p(x)=1/x and q(x)=1/4x

I want to know if these are analytic.
My definition of analytic is this:
Analytic means can be expanded in a taylor series about x=x0, with non zero radius of convergence)

reason for asking is I want to determine whether I should use basic power series or method of frobenius for the DE:
y'' + (1/x)y'+(1/4x)y = 0

The Attempt at a Solution

I'm guessing that since p and q cannot be expanded in a taylor series, that makes them non-analytic?

 

[lanedance]

not at x = 0, i don't think so

 

[t_n_p]

which is what I thought, which makes them singular points.

Interestingly, if I use the Frobenius method, my solution ends up being the general power series :S

 

[lanedance]

they are regular singular points though

 

[t_n_p]

yes sorry.
regular singular points which corresponds to the use of method of frobenius