Function of exponential type
From Encyclopedia of Mathematics
An entire function satisfying the condition
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If is represented by a series
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then
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The simplest examples of functions of exponential type are ,
,
, and
.
A function of exponential type has an integral representation
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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) MR0156975 Zbl 0152.06703 |
Comments
References
[a1] | R.P. Boas, "Entire functions" , Acad. Press (1954) MR0068627 Zbl 0058.30201 |
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
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