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
 |
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) 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