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→Infinite Product representation of entire functions
where ''m'' is the multiplicity of the zero of ''f''(''z'') at the origin, and φ(''z'') is some [[entire function]].
where ''m'' is the multiplicity of the zero of ''f''(''z'') at the origin, and φ(''z'') is some [[entire function]].
One spectacular result of the ''Weierstrass Factorization Theorem'' is the representation of the [[Riemann Zeta Function]] <math>\zeta</math> as a product over its non-trivial zeros ''n'', known as the ''Hadamard Product'':
:<math>\zeta(z) = \frac{e^{\left [ ln 2 \pi - 1 - \frac{\gamma}{2} \right ]z}}{2(z-1) \Gamma (1+\frac{z}{2})} \prod_{n} (1-\frac{z}{n})e^{\frac{z}{n}}</math>
where <math>\gamma</math> is the [[Euler-Mascheroni constant]] and <math>\Gamma</math> is the [[Gamma function]].
[[category:mathematics]]
[[category:mathematics]]
[[category:complex analysis]]
[[category:complex analysis]]