# Function of exponential type

From Encyclopedia of Mathematics

An entire function satisfying the condition

If is represented by a series

then

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 .

#### References

[1] | B.Ya. Levin, "Distribution of zeros of entire functions" , Amer. Math. Soc. (1964) (Translated from Russian) |

#### Comments

#### References

[a1] | R.P. Boas, "Entire functions" , Acad. Press (1954) |

**How to Cite This Entry:**

Function of exponential type.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Function_of_exponential_type&oldid=12134

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