I am trying to evaluate the following sum:
$\sum_{p = p_0}^{\infty} \frac{x^p}{p^{3/2}} $
where $p_0$ is some integer larger than one and $x$ is smaller than one.
Sums like $\sum_{p = p_0}^{\infty} px^p$ or $\sum_{p = p_0}^{\infty} \frac{x^p}{p} $ can be evaluated by switching sums and integrals, but I don't know how to deal with the $p^{3/2}$. Can anyone help me?