Difference between revisions of "Barnes G"

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=Properties=
 
=Properties=
{{:Barnes G at z+1 in terms of Barnes G and gamma}}
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[[Barnes G at z+1 in terms of Barnes G and gamma]]<br />
{{:Barnes G at positive integer}}
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[[Barnes G at positive integer]]<br />
 
 
[[Category:SpecialFunction]]
 
  
 
=References=
 
=References=
 
[http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=PPN600494829_0031%7CLOG_0022 The theory of the $G$-function by E.W. Barnes]
 
[http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=PPN600494829_0031%7CLOG_0022 The theory of the $G$-function by E.W. Barnes]
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[[Category:SpecialFunction]]
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[[Category:Definition]]

Latest revision as of 05:48, 6 June 2016

The Barnes $G$ function is defined by the following Weierstrass factorization: $$G(1+z)=(2\pi)^{\frac{z}{2}} \exp \left( - \dfrac{z+z^2(1+\gamma)}{2} \right) \displaystyle\prod_{k=1}^{\infty} \left\{ \left( 1+\dfrac{z}{k} \right)^k \exp \left( \dfrac{z^2}{2k}-z \right) \right\},$$ where $\exp$ denotes the exponential function and $\gamma$ denotes the Euler-Mascheroni constant.

Properties

Barnes G at z+1 in terms of Barnes G and gamma
Barnes G at positive integer

References

The theory of the $G$-function by E.W. Barnes