Difference between revisions of "Hyperfactorial"

From specialfunctionswiki
Jump to: navigation, search
 
(3 intermediate revisions by the same user not shown)
Line 5: Line 5:
 
<gallery>
 
<gallery>
 
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: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 $H(n)$.
 
 
</gallery>
 
</gallery>
 
</div>
 
</div>
  
 
=Properties=
 
=Properties=
[[Hyperfactorial at nonintegers]]<br />
+
[[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