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#### chisigma

##### Well-known member

- Feb 13, 2012

- 1,704

Infinite Series Conditional Converging

... about the following two variables function...

$\displaystyle \sigma(x,y)= \sum_{k=1}^{\infty} \frac{1}{(k+x)\ (k+y)}$ (1)

... and in particular it has been requested if the domain of $\sigma(*,*)$ must be restricted to the quarter of plane $x>0,y>0$ or may be that, with the exception of a discrete set of points, it could be also $x \le 0, y \le 0$. What is Your answer?...

Kind regards

$\chi$ $\sigma$