Changes

*According to elementary factors, it is a special case of the double gamma function.

*According to elementary factors, it is a special case of the double gamma function.

*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})\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>

 

{{(1+\frac{z}{k})}^k

{{(1+\frac{z}{k})}^k