Function of exponential type
An entire function satisfying the condition
If is represented by a series
The simplest examples of functions of exponential type are , , , and .
A function of exponential type has an integral representation
where is the function associated with in the sense of Borel (see Borel transform) and is a closed contour enclosing all the singularities of .
|||B.Ya. Levin, "Distribution of zeros of entire functions" , Amer. Math. Soc. (1964) (Translated from Russian)|
|[a1]||R.P. Boas, "Entire functions" , Acad. Press (1954)|
Function of exponential type. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Function_of_exponential_type&oldid=12134