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*Formally, the Barnes G-function is defined in the following Weierstrass product form:
 
*Formally, the Barnes G-function is defined in the following Weierstrass product form:
 
<math>G(1+z)={(2\pi)}^\frac{z}{2}exp(-\frac{z+z^2(1+\gamma)}{2})</math>
 
<math>G(1+z)={(2\pi)}^\frac{z}{2}exp(-\frac{z+z^2(1+\gamma)}{2})</math>
*<math>\prod_{k=1}^\infty {{(1+\frac{z}{k})}^k exp(\frac {z^2}{2k}-z)}</math>
+
*<math>\prod_{k=1}^\infty {{{(1+\frac{z}{k})}^k exp(\frac {z^2}{2k}-z)}}</math>
 
<math> exp(\frac {z^2}{2k}-z)</math>
 
<math> exp(\frac {z^2}{2k}-z)</math>
    
{{(1+\frac{z}{k})}^k
 
{{(1+\frac{z}{k})}^k
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