As i already know, behaviour of meromorphic function is completly determined by its values on some line on the domain.
Consider meromorphic function $f$ Suppose that we know everything about behaviour of $f$ on real axis.
How to tell whether $f$ has pole or not.
Of course if $f$ blows up at point $a\in \mathbb{R}$ then it is a pole. I would like to consider how does pole which is out of line affect on behaviour of $f$
The answer is that you can't in general : the analytic continuation isn't continuous with respect to the obvious parameters of the function.