To define my own math operators, I usually use amsmath's \DeclareMathOperator. However, with \DeclareMathOperator{\Res}{Res} does not give me the desired "limits" under the operator even in displayed math.
Searching this site, I found \operatorname* (and \operatornamewithlimits) which implements the desired behavior.
\begin{equation}
\operatorname*{Res}_{x = y} \frac{1}{x - y}
= 1.
\end{equation}
gives
However, I'm still unsure if this can or should somehow be combined with \DeclareMathOperator and generally when to choose \operatorname* over \DeclareMathOperator (besides this particular case).
\DeclareMathOperator*.