# Math Help - radius of covergentia

could you determinate for what values os q and x the serie is convergent.

$\sum _{z=1}^{\infty } \frac{(-1)^{-1+z} q^{-x (1+2 z)^2}}{(1+2 z)^2}\simeq \frac{5}{6}-\text{Catalan}-\frac{q^{-9 x}}{12}+\frac{q^{-x}}{4}+\frac{1}{4} \sqrt{\pi } \sqrt{x} \text{Erf}\left[\sqrt{x} \sqrt{\text{Log}[q]}\right] \sqrt{\text{Log}[q]}-\frac{1}{4} \sqrt{\pi } \sqrt{x} \text{Erf}\left[3 \sqrt{x} \sqrt{\text{Log}[q]}\right] \sqrt{\text{Log}[q]}-\frac{1}{3} x^2 \text{Log}[q]^2+\frac{34}{15} x^3 \text{Log}[q]^3-\frac{163}{84} x^4 \text{Log}[q]^4$
and check if the solution is good
thanks

2. ## Re: radius of covergentia

Nobody's going to solve that beast for you. Why don't you tell us what you tried and where you got stuck, and maybe we can give some hints.

3. ## Re: radius of covergentia

Use Cauchy-Hadamard theorem and look at the cases $x<0$, $x=0$ and $x>0$.