Consider the power series S(x) = _ n=0 ^ n^2 x^ 2n 3^n in a dimensionless variable

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Mathematical Methods for Physics, Ch Series, limits and controlled approximation

Problem

Consider the power series

S(x) = \sum_{n=0}^{\infty} \frac{n^2 x^{2n}}{3^n}

in a dimensionless variable

x

. Find the radius of convergence

R_{\mathrm{c}}

of this series.

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