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[tex]\mbox {Suppose I have: } \sum_{n=1}^\infty (\frac {x} {3})^{2n} [/tex]

[tex]\mbox{Can I define } y= \frac {x} {3} [/tex]

[tex]

a_k(y) = \left\{

\begin{array}{c l}

(y)^k, & \mbox{if } k= 2n\\

\\

(0)^k, & \mbox{otherwise}

\end{array}

\right.

[/tex]

[tex] \mbox {And then use all the cool properties of power series on } \sum_{k=1}^\infty a_k(y)[/tex]

[I edited my question]

[tex]\mbox{Can I define } y= \frac {x} {3} [/tex]

[tex]

a_k(y) = \left\{

\begin{array}{c l}

(y)^k, & \mbox{if } k= 2n\\

\\

(0)^k, & \mbox{otherwise}

\end{array}

\right.

[/tex]

[tex] \mbox {And then use all the cool properties of power series on } \sum_{k=1}^\infty a_k(y)[/tex]

[I edited my question]

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