Let 
be an entire function of finite
order 
and 
the zeros of 
, listed with multiplicity,
then the rank 
of 
is defined as the least positive integer such that
 |
(1)
|
Then the canonical Weierstrass product is given by
 |
(2)
|
and 
has degree 
. The genus 
of 
is then defined as 
, and the Hadamard factorization theory states that
an entire function of finite
order 
is also of finite genus 
, and
 |
(3)
|
