(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Write [tex]\displaystyle \sum_{k=0}^{\infty} \frac{1}{9^k (\frac{2}{3})_k} \frac{w^{3k}}{k!}[/tex] in terms of the Gauss hypergeometric series of the form [itex]_2 F_1(a,b;c;z)[/itex].

2. Relevant equations

The Gauss hypergeometric series is http://img200.imageshack.us/img200/5992/gauss.png [Broken]

3. The attempt at a solution

It's nearly a series of that form if I put [itex]z=w^3[/itex] and [itex]k=n[/itex] but how do I get the [itex]9^{-k} = 3^{-k}3^{-k}[/itex] factors in terms of shifted factorials (that is if I need to)?

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# Homework Help: Writing this series as a hypergeometric series

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