- #1
Ted123
- 446
- 0
Homework Statement
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].
Homework Equations
The Gauss hypergeometric series is http://img200.imageshack.us/img200/5992/gauss.png
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)?
Last edited by a moderator: