Hyperfactorial

Hyperfactorial[n]

gives the hyperfactorial function .

Details

  • Mathematical function, suitable for both symbolic and numeric manipulation.
  • Hyperfactorial is defined as for positive integers .
  • Hyperfactorial is defined as for positive integers and is otherwise defined as InterpretationBox[H, Hyperfactorial, Editable -> False, Selectable -> False](z)=(z/(sqrt(2 pi)))^z exp(1/2 z (z-1)+TemplateBox[{{-, 2}, z}, PolyGamma2]).
  • The hyperfactorial function satisfies .
  • Hyperfactorial can be evaluated to arbitrary numerical precision.
  • Hyperfactorial automatically threads over lists.

Examples

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Basic Examples  (3)

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Scope  (6)

Applications  (1)

Properties & Relations  (2)

See Also

BarnesG  Gamma  Glaisher

Introduced in 2008
(7.0)