analytic function


Also found in: Dictionary, Wikipedia.

analytic function

[‚an·əl′id·ik ′fuŋk·shən]
(mathematics)
A function which can be represented by a convergent Taylor series. Also known as holomorphic function.
References in periodicals archive ?
Let H(U) be the class of analytic functions in the open unit disk U:= {z [member of] C: |z| < 1} and H[a, n] be the subclass of H(U) consisting of the form
If f is an analytic function in the interior of [[epsilon].sub.[rho]], then it can be expanded as
Let y be a nonzero analytic function on [C.sup.N] and [PHI] be an analytic self-map of [C.sup.N].
A fixed point method use an iteration function (IF) which is an analytic function mapping its domain of definition into itself.
For functions p and q, where p(0) = q(0) = 0, we write p [??] q (i.e., p is subordinate to q) if there exists an analytic function [omega] with [omega] (0) = 0 and [absolute value of ([omega](z))] < 1 so that p(z) = q([omega](z)) in D.
Based on the analytic function z([zeta]), the one-to-one corresponding relations between [theta] and [alpha] are determined as
In the field of Geometric Function Theory, various subclasses of the normalized analytic function class A have been studied from different viewpoints.
Define an analytic function p : D [right arrow] C by
By noticing that [p.sub.k] (x, y), [q.sub.k] (x, y) are both analytic functions, we rewrite system (10) into the following form:
Since the hypergeometric series in (83) converges absolutely in D, it follows that F([beta], [gamma], [delta]; z) defines an analytic function in D and plays an important role in the theory of univalent functions.
This class is called starlike class of analytic function, let f [member of] [gamma].