properties of entire functions
If, conversely, such a power series converges for every complex value , then the sum of the series (http://planetmath.org/SumFunctionOfSeries) is an entire function.
The entire functions may be divided in two disjoint :
a) The entire rational functions, i.e. polynomial functions; in their series there is an such that .
A consequence of Liouville’s theorem: If is a non-constant entire function and if and are two arbitrarily great positive numbers, then there exist such points that
This that the non-constant entire functions are unbounded (http://planetmath.org/BoundedFunction).
The sum (http://planetmath.org/SumOfFunctions), the product (http://planetmath.org/ProductOfFunctions) and the composition of two entire functions are entire functions.
The ring of all entire functions is a Prüfer domain.
- 1 O. Helmer: “Divisibility properties of integral functions”. – Duke Math. J. 6 (1940), 345–356.
|Title||properties of entire functions|
|Date of creation||2013-03-22 14:52:09|
|Last modified on||2013-03-22 14:52:09|
|Last modified by||pahio (2872)|
|Defines||entire rational function|
|Defines||entire transcendental function|