K-Function
KFunction
KFunctionReIm
KFunctionContours
For positive integer n, the K-function is defined by
K(n) = 1^12^23^3...(n-1)^(n-1)
(1)
= H(n-1),
(2)
where the numbers H(n)=K(n+1) are called hyperfactorials by Sloane and Plouffe (1995). It is related to the Barnes G-function by
![画像: K(n)=([Gamma(n)]^(n-1))/(G(n)).](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/K-Function/NumberedEquation1.svg){kind=link}
The first few values of K(n) for n=1, 2, ... are 1, 1, 4, 108, 27648, 86400000, 4031078400000, ... (OEIS A002109).
See also
Barnes G-Function, Glaisher-Kinkelin Constant, HyperfactorialExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Sloane, N. J. A. Sequence A002109/M3706 in "The On-Line Encyclopedia of Integer Sequences."Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, p. 264, 1990.Referenced on Wolfram|Alpha
K-FunctionCite this as:
Weisstein, Eric W. "K-Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/K-Function.html