- In mathematics, and more
specifically number theory, the
hyperfactorial of a
positive integer n {\displaystyle n} is the
product of the
numbers of the...
- the K-function,
typically denoted K(z), is a
generalization of the
hyperfactorial to
complex numbers,
similar to the
generalization of the
factorial to...
- an
abundant number. a
semiperfect number. a
tetranacci number. the
hyperfactorial of 3
since it is of the form 1 1 ⋅ 2 2 ⋅ 3 3 {\displaystyle 1^{1}\cdot...
-
distribution Gamma function Gaussian binomial coefficient Gould's
sequence Hyperfactorial Hypergeometric distribution Hypergeometric function identities Hypergeometric...
-
sphenic number and a
Harshad number. It is the sum of the
first four
hyperfactorials,
including H(0). At 114, the
Mertens function sets a new low of -6...
- 934,656 = 92162 = 964 85,766,121 = 92612 = 4413 = 216 86,400,000 =
hyperfactorial of 5; 11 × 22 × 33 × 44 × 55 87,109,376 = 1-automorphic
number 87,539...
- polynomials, and in the
factorial moments of
random variables.
Hyperfactorials The
hyperfactorial of n {\displaystyle n} is the
product 1 1 ⋅ 2 2 ⋯ n n {\displaystyle...
- e^{-{\tfrac {n^{2}}{4}}}}}}
where H ( n ) {\displaystyle H(n)} is the
hyperfactorial: H ( n ) = ∏ i = 1 n i i = 1 1 ⋅ 2 2 ⋅ 3 3 ⋅ . . . ⋅ n n {\displaystyle...
-
factorials grow much more
quickly than
regular factorials or even
hyperfactorials. The
number of
digits in the
exponential factorial of 6 is approximately...
- instance, new
variants of Wilson's
theorem stated in
terms of the
hyperfactorials, subfactorials, and
superfactorials are
given in. For
integers k ≥...
