2 problems

Let $k$ be algebraically closed, let $r,s\geq 1$, and let $p$ be relatively prime to $r$ and $s$. Let … be a formal Laurent series in $k((1/t))$ with $a_{-s}\neq 0$, and let…

Let $k$ be algebraically closed. For a Laurent series … with $a_{-s}\neq 0$, define its formal Legendre transformation $L_f(t')$ by … Write $L_f(t')$ as a Laurent series in…