Editing Cousin problems (section)

{{Short description|Make a meromorphic function from local data in multiple variables}}
In [[mathematics]], the '''Cousin problems''' are two questions in [[Function of several complex variables|several complex variables]], concerning the existence of [[meromorphic function]]s that are specified in terms of local data. They were introduced in special cases by [[Pierre Cousin (mathematician)|Pierre Cousin]] in 1895. They are now posed, and solved, for any [[complex manifold]] ''M'', in terms of conditions on ''M''.

For both problems, an [[open cover]] of ''M'' by sets ''U<sub>i</sub>'' is given, along with a meromorphic function ''f<sub>i</sub>'' on each ''U<sub>i</sub>''.