I am interested in finding the following infinite sums in order to reparameterize a distribution function.
$\sum_{n=0}^{\infty} \theta^{n}q^{n(n-2)/2} $
where $\theta>0$ and $1>q>0$
and
$\sum_{n=0}^{\infty} n\theta^{n}q^{n(n-2)/2} $
where $\theta>0$ and $1>q>0$