meromorphic

[mer-uh-mawr-fik]

adjective

Mathematics.

1. of or relating to a function that is analytic, except for poles, in a given domain.

Word History and Origins

Origin of meromorphic¹

Probably earlier than 1885–90; mero- + -morphic

Example Sentences

Dr. Joshi used the vivid image of volcanoes dotting a landscape to describe meromorphic functions.

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It says that you can basically recreate a meromorphic function if you know the locations of the poles and the behavior, or to use Dr. Joshi’s word, strength of the function around the poles.

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The single valued functions which occur, as explained above, in the inversion of algebraic integrals of the first kind, for p > 1, are meromorphic.

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In the case of p = 1, all meromorphic functions periodic with the same two periods have been shown to be rational functions of two of them connected by a single algebraic equation; in the same way all meromorphic functions of p variables, periodic with the same sets of simultaneous periods, 2p sets in all, can be shown to be expressible rationally in terms of p + 1 such periodic functions connected by a single algebraic equation.

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Let x1, ... xp, y denote p + 1 such functions; then each of the partial derivatives dxi/∂ui will equally be a meromorphic function of the same periods, and so expressible rationally in terms of x1, ... xp, y; thus there will exist p equations of the form dxi = R1du1 + ...

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