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while the [[gamma function]] <math>\Gamma</math> has factorization
<math display=block>\frac{1}{\Gamma (z)}=e^{\gamma z}z\prod_{n=1}^{\infty }\left ( 1+\frac{z}{n} \right )e^{-z/n},</math>
where <math>\gamma</math> is the [[Euler–Mascheroni constant]].
<math display=block>\frac{1}{\Gamma(s-z)\Gamma(s+z)} = \frac{1}{\Gamma(s)^2}\prod_{n=0}^\infty \left( 1 - \left(\frac{z}{n+s} \right)^2 \right) </math>
for <math>s=\tfrac{1}{2}</math>.
===Hadamard factorization theorem===
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