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Guillera & Sondow gave

[tex]e^{x}=\prod_{n=1}^{\infty}\left(\prod_{k=1}^{n} (1+kx)^{(-1)^{k+1}\left(\begin{array}{c}n\\k\end{array}\right)} \right) ^{\frac{1}{n}}[/tex]

for [tex]x\geq 0[/tex], to which I add

[tex]\boxed{\frac{e^{u}\Gamma (u)}{\sqrt{2\pi e}}=\prod_{n=0}^{\infty}\left(\prod_{k=0}^{n} (k+u)^{(-1)^{k}\left(\begin{array}{c}n\\k\end{array}\right) (k+u)} \right) ^{\frac{1}{n+1}}}[/tex]

for [tex]\mbox{Re} \geq 0[/tex].

-Ben Orin

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# An Infinite Product

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