Difference between revisions of "Hyperfactorial"

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File:Hyperfactorialplot.png|Plot of hyperfactorial on $[-1,2]$.
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File:Loghyperfactorialplot.png|Plot of the [[logarithm]] of the hyperfactorial on $[0,10]$ (we plot the log because $H$ increases too fast to plot alone).
File:Domain coloring hyperfactorial.png|[[Domain coloring]] of [[analytic continuation]] of $H(n)$.
 
 
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=Properties=
 
=Properties=
[[Hyperfactorial at nonintegers]]<br />
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[[Hyperfactorial in terms of K-function]]<br />
  
 
=References=
 
=References=
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 19:39, 25 September 2016

The hyperfactorial is defined for integers $n=1,2,3,\ldots$ by the formula $$H(n)=\displaystyle\prod_{k=1}^n k^k.$$

Properties

Hyperfactorial in terms of K-function

References