# holomorphic function

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Related to holomorphic function: Meromorphic function

## holomorphic function

[¦häl·ō¦mȯr·fik ′fəŋk·shən]
(mathematics)
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9-12], for the definition of holomorphic functions see e.
where P(t,X) is a holomorphic function on some domain D [subset] C with respect to t and polynomial in the variable X of degree larger than 2.
d]J(c) [not equal to] 0, there exists a holomorphic function g guaranteed by the implicit function theorem such that in some open ball around c, J(X, g(X)) = 0.
Suppose that f (z) is a holomorphic function defined in an open neighborhood of the set {1} [union] {[absolute value of z]} [subset] C.
is 1-summable in the direction [theta] if there exists a holomorphic function f which is 1-Gevrey asymptotic to [?
x](N') and the space Hol0(N) of holomorphic function on a neighborhood of zero of N.
We recall that a Pick function is a holomorphic function [phi] in the upper half-plane H with [?
The characteristic function as defined by Nevanlinna for a holomorphic function f : C [approaches] C is
c) For every pair of distinct points x [not equal to] y in X there is a holomorphic function f [member of] O (X) such that f (x) [not equal to] f (y).
1], can be continued as a holomorphic function to the annulus 1 < |z| < 1/[p.
This kernel has a unique extension to holomorphic function on [[?

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