Editing Hyperfactorial (section)

==Interpolation and approximation==
The hyperfactorials were studied beginning in the 19th century by [[Hermann Kinkelin]]{{r|kinkelin|wilson}} and [[James Whitbread Lee Glaisher]].{{r|glaisher|wilson}} As Kinkelin showed, just as the [[factorial]]s can be [[continuous function|continuously]] interpolated by the [[gamma function]], the hyperfactorials can be continuously interpolated by the [[K-function]].{{r|kinkelin}}

Glaisher provided an [[asymptotic analysis|asymptotic]] formula for the hyperfactorials, analogous to [[Stirling's formula]] for the factorials:
<math display=block>H(n) = An^{(6n^2+6n+1)/12}e^{-n^2/4}\left(1+\frac{1}{720n^2}-\frac{1433}{7257600n^4}+\cdots\right)\!,</math>
where <math>A\approx 1.28243</math> is the [[Glaisher–Kinkelin constant]].{{r|summability|glaisher}}