Can anyone tell me how to compute this sum over infinite series containing log like this-
$$D(x)=\sum_{n=-\infty} ^\infty \ln\left(\mu\sqrt{ (x_0-n\beta)^2+x_1^2}\right)$$.
The answer of the sum is the following. any clue how to do it?
$$D(x)=\sum_{n=-\infty} ^\infty \ln\left(\mu\sqrt{ (x_0-n\beta)^2+x_1^2}\right)=\ln\left(\mu\beta\sqrt{\cosh(\frac{2x_1\pi}{\beta}) - \cos(\frac{2x_0\pi}{\beta})}\right)$$.
Thanks in advance.