Difference between revisions of "Hyperfactorial"
From specialfunctionswiki
(Created page with "$$H(n)=\displaystyle\prod_{k=1}^n k^k$$") |
|||
| (9 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | $$H(n)=\displaystyle\prod_{k=1}^n k^k$$ | + | The hyperfactorial is defined for integers $n=1,2,3,\ldots$ by the formula |
| + | $$H(n)=\displaystyle\prod_{k=1}^n k^k.$$ | ||
| + | |||
| + | <div align="center"> | ||
| + | <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). | ||
| + | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =Properties= | ||
| + | [[Hyperfactorial in terms of K-function]]<br /> | ||
| + | |||
| + | =References= | ||
| + | |||
| + | [[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 $$H(n)=\displaystyle\prod_{k=1}^n k^k.$$
Plot of the logarithm of the hyperfactorial on $[0,10]$ (we plot the log because $H$ increases too fast to plot alone).
Properties
Hyperfactorial in terms of K-function
