# 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.

## 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 ?
Nevanlinna proved that a non-constant meromorphic function is uniquely determined by the inverse image of 5 distinct values (including the infinity) IM.
Denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the set of poles of the meromorphic function F([alpha]) and by p([zeta]) the order of the pole [zeta] for [zeta] [member of] P.
For any nonconstant meromorphic function h(z)wedenoteby S(r, h) any quantity satisfying
Control of delay systems--A meromorphic function approach.
On starlikeness and close to convexity of certain meromorphic function, J.
If [member of] is a meromorphic function, having [gamma] as a pole, we denote by [[G([lambda])].
nn]} converges to a meromorphic function in capacity, which means away from exceptional sets that may vary from one value of n to the next and whose capacities decrease exponentially to 0 as n [right arrow] [infinity] [1, 18, 20, 25].
Among the poles of the meromorphic function Z(s) are the roots p of the Riemann zeta function in the critical strip 0 < [sigma]< 1, which is clear from Eq.
Kulkarni, Subclasses of meromorphic function defined by Ruscheweyh derivative for positive coefficients, Acta Cienc.
s](n) can be continued to the whole complex plane as a meromorphic function with simple poles 1, 1/2; -1/2, -3/2, -5/2, .
a](z) to a meromorphic function and the determination of its poles.

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