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→See also: link to the article about the Wallis product |
→Hadamard factorization theorem: explain square bracket, from entire function Tags: Mobile edit Mobile web edit Advanced mobile edit |
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If {{math|''ƒ''}} is an entire function of finite [[Entire function|order]] {{math|''ρ''}} and {{math|''m''}} is the order of the zero of {{math|''ƒ''}} at {{math|''z''}}={{math|''0''}}, then it admits a factorization
: <math>f(z) = z^m e^{g(z)} \displaystyle\prod_{n=1}^\infty E_{p}\!\!\left(\frac{z}{a_n}\right)</math>
where {{math|''g''(''z'')}} is a polynomial of degree {{math|''q''}}, {{math|''q'' ≤ ''ρ''}} and {{math|1=''p'' = [''ρ'']}} is the integer part of {{math|''ρ''}}.<ref name="conway" />
==See also==
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