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Convergence of Infinite Composition of Entire Functions
Infinite Composition Entire Functions
2010/12/6
The purpose of the present article is to obtain the condition that the function defined by infinite composition of entire functions be-comes an entire function. Moreover, as an example of such functio...
Let f be a transcendental entire function and let A(f) denote the set of points that escape to infinity ‘as fast as possible’ under iteration. By writing A(f) as a countable union of closed sets, call...
Normal Families and Uniqueness of Entire Functions and Their Derivatives
entire function normal family unicity theorem
2007/12/10
Let $f$ be a nonconstant entire function; let $k\ge 2$ be a positive integer; and let $a$ be a nonzero complex number. If $f(z)=a$ $\Longrightarrow $ $f'(z)=a$, and $f'(z)=a$ $\Longrightarrow $ $f^{(k...