# Meromorphic Function

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## meromorphic function

[¦mer·ə¦mȯr·fik ′fəŋk·shən]
(mathematics)
A function of complex variables which is analytic in its domain of definition save at a finite number of points which are poles.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Meromorphic Function

a function that can be represented in the form of a quotient of two entire functions, that is, the quotient of the sums of two everywhere convergent power series. Meromorphic functions include many important functions and classes of functions (rational functions, trigonometric functions, elliptic functions, the gamma function, the zeta function).

References in periodicals archive ?
For [omega] [member of] [(C - [square root of (-1)]R).sup.r], [[GAMMA].sub.r](s, [omega]) and [S.sub.r](s, [omega]) are meromorphic functions in s [member of] C.
where j = 1,...,p, l = 1,...,m, and [[phi].sub.i] are real meromorphic functions. The word 'explicit' means that the variable [y.sub.i](t + [n.sub.i]) does not appear on the right-hand side of the ith equation, i.e.
A meromorphic function p(z) [??] p(z, [g.sub.2], [g.sub.3]) with double periods 2[v.sub.1], 2[v.sub.2], which satisfies the equation
Suppose that f(z) and g(z) are two nonconstant meromorphic functions. We define a(z) as a meromorphic function or a finite complex number.
Let a and b be two distinct finite values and f be a meromorphic function in the complex plane with finitely many poles.
The restriction of meromorphic function [[gamma].sub.c] on [C.sub.q] we call Complex Characteristic Function (Complex CF) .
Weierstrass elliptic function p(z) := p(z, [g.sub.2], [g.sub.3]) is a meromorphic function with double periods 2[[omega].sub.1], 2[[omega].sub.2] and satisfying the equation
Note that [[zeta].sub.E,q](s,x) is a meromorphic function on C.
Let f be a transcendental meromorphic function in C, all but finitely many of whose zeros are multiple, and let R([not equivalent to] 0) be a rational function.
It is well known that this function extends to a meromorphic function of [xi] [member of] [V.sup.*.sub.C].
Example in Subsection 3.1 takes the same meromorphic function as in  to compare the fast IPRM and the G-IPRM proposed in .
For any nonconstant meromorphic function h(z)wedenoteby S(r, h) any quantity satisfying

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