Hyperfactorial

Hyperfactorial[n]
gives the hyperfactorial function .

DetailsDetails

  • 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.
Introduced in 2008
(7.0)