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