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) MR0156975 Zbl 0152.06703|
|[a1]||R.P. Boas, "Entire functions" , Acad. Press (1954) MR0068627 Zbl 0058.30201|
Function of exponential type. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Function_of_exponential_type&oldid=24449