meromorphic function
[ˌmerəˈmɔ:fik ˈfʌŋkʃən]
In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points (the poles of the function), at each of which the function must have a Laurent series. (The terminology comes from the Ancient Greek meros ([meaning part, as opposed to holos (?λο?]), meaning whole.