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Date: 1-11-2018
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Date: 24-10-2018
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Date: 24-10-2018
733
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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) |
REFERENCES:
Krantz, S. G. "The Hadamard Factorization Theorem." §9.3.5 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 121-122, 1999.
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