BarnesG

BarnesG[z]

gives the Barnes G-function .

Details

  • BarnesG is also known as the double gamma function.
  • Mathematical function, suitable for both symbolic and numeric manipulation.
  • The Barnes G-function is defined as G(n)=product_(k=1)^(n-1)TemplateBox[{k}, Gamma] for positive integers and is otherwise defined as TemplateBox[{z}, BarnesG]=(2 pi)^(z/2) exp((z-1) (TemplateBox[{z}, LogGamma]-z/2)-TemplateBox[{{-, 2}, z}, PolyGamma2]).
  • The Barnes G-function satisfies .
  • BarnesG can be evaluated to arbitrary numerical precision.
  • BarnesG automatically threads over lists.

Examples

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Basic Examples  (2)

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Scope  (6)

Applications  (2)

Properties & Relations  (2)

Neat Examples  (1)

See Also

Gamma  Hyperfactorial  LogBarnesG  Glaisher  DiscreteRatio

Introduced in 2008
(7.0)