Function of exponential type

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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 .


[1] 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)
How to Cite This Entry:
Function of exponential type. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.F. Leont'ev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article