How to find the following summation How to find the following sum $$\sum\limits_{n=1}^{\infty}\dfrac{\left(\dfrac{3-\sqrt{5}}{2}\right)^n}{n^3}$$
I have tried by rationalizing. But after that I got stuck.

By definition, for $|r|<1$, 
$$ \sum_{n=1}^\infty r^n/n^3 = \text{polylog}(3,r)$$
This is not an elementary function.
