How to simplify this summation, or express as integral? $\sum_{t=-\infty}^\infty\frac1{\sqrt{(t+ax)^2+4}}$ How to simplify this summation, or express as integral?
$$f(x)=\sum_{t=-\infty}^\infty\frac1{\sqrt{(t+ax)^2+4}}$$
$a$ is a constant, say, 24.
$$f(x)=\sum_{t=-\infty}^\infty\frac1{\sqrt{(t+24x)^2+4}}$$

Just to make an answer from sos440's comment: From the integral test you get:
$$\sum_{t=1}^\infty\frac1{\sqrt{(t+24x)^2+4}} > \int_1^\infty  \frac1{\sqrt{(t+24x)^2+4}} dt = \infty$$
because $\frac1{\sqrt{(t+24x)^2+4}} \approx \frac 1x$  for $x\rightarrow\infty$ and $\int_1^\infty \frac 1x dx$ diverges. Because each summand of $f(x)$ is positive, also $$\sum_{t=-\infty}^\infty\frac1{\sqrt{(t+24x)^2+4}} = \infty$$.
