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Manuals/calci/GFUNCTION
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Revision as of 22:46, 8 August 2017
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22:46, 8 August 2017
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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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