An extension of the -function
(1) |
(2) |
(3) |
The -function is given by the integral
(4) |
(5) |
(6) |
(7) |
(8) | |||
(9) | |||
(10) |
The first few values of for , 3, ... are 1, 4, 108, 27648, 86400000, 4031078400000, ... (Sloane's A002109). These numbers are called Hyperfactorials by Sloane and Plouffe (1995).
See also G-Function, Glaisher-Kinkelin Constant, Hyperfactorial, Stirling's Series
References
Sloane, N. J. A. Sequence
A002109/M3706
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
© 1996-9 Eric W. Weisstein