meromorphic

adjective

mer·​o·​mor·​phic ˌmer-ə-ˈmȯr-fik 

: relating to or being a function of a complex variable that is analytic everywhere in a region except for singularities at each of which infinity is the limit and each of which is contained in a neighborhood where the function is analytic except for the singular point itself

Word History

Etymology

mero- + -morphic

First Known Use

circa 1890, in the meaning defined above