Difference between revisions of "Function of exponential type"
From Encyclopedia of Mathematics
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− | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> | + | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> B.Ya. Levin, "Distribution of zeros of entire functions" , Amer. Math. Soc. (1964) (Translated from Russian) {{MR|0156975}} {{ZBL|0152.06703}} </TD></TR></table> |
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− | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> | + | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> R.P. Boas, "Entire functions" , Acad. Press (1954) {{MR|0068627}} {{ZBL|0058.30201}} </TD></TR></table> |
Revision as of 16:57, 15 April 2012
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=24449
Function of exponential type. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Function_of_exponential_type&oldid=24449
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