How to find an entire function $f(z)$ such that $f(n) = \sqrt {|n|}$ for every integer $n$?
Now my thinking is to create a series $\displaystyle\sum_{k=-\infty}^\infty f_{k}(z)$ such that $f_{k}(z)=\sqrt{|k|}$ and the series is convergent for every $z$.
Thanks for any help