Power Series Solutions to Linear Differential Equations: Proof of Analyticity

We prove that near an ordinary point the solution to a second order linear differential equation has a valid Taylor series representation in a neighborhood of the ordinary point. We assume that the differential equation has the form y''+ p(x)y'+ q(x)y = 0, where p and q are analytic functions. We use the Cauchy product formula an estimate the coefficients of the formal expansion of y.
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