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K-Function

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The K-function has the values

K(n)=1^12^23^3...(n-1)^(n-1)
(1)
=H(n-1)
(2)

for positive integers n, 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

K(n)=([Gamma(n)]^(n-1))/(G(n)).
(3)

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, Hyperfactorial

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References

Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, 1995.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.

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K-Function

Cite this as:

Weisstein, Eric W. "K-Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/K-Function.html

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