I've two complex functions:
1) $f(z) = \frac 1 {\sin(πz^2)}$.
It has simple poles at $ z = \sqrt n$ for all integers $n$ except $0$.
2) $f(z) = \frac z {\sin πz^2}.$
It has poles of order two at $z = \sqrt n$ for all integers $n$ except $0$.
I've tried Laurent series expansion, and residue formation, but I can't prove the results. Although I've proved for $z=0$.
Please guide me through this problem. What might I be missing?