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HYPERFACTORIAL

Hyperfactorial

Number computed as a product of powers

In mathematics, and more specifically number theory, the hyperfactorial of a positive integer n {\displaystyle n} is the product of the numbers of the

Hyperfactorial

K-function

Concept in mathematics

the K-function, typically denoted K(z), is a generalization of the hyperfactorial to complex numbers, similar to the generalization of the factorial to

K-function

Combinatorics

Branch of discrete mathematics

identities Factorials & approximations Factorial · Bhargava factorial · Hyperfactorial · Alternating factorial · Factorial moment · Factorial number system

Combinatorics

Factorial

Product of numbers from 1 to n

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

Factorial

Binomial coefficient

Number of subsets of a given size

identities Factorials & approximations Factorial · Bhargava factorial · Hyperfactorial · Alternating factorial · Factorial moment · Factorial number system

Binomial coefficient

Binomial_coefficient

108 (number)

Natural number

11 (9911), 17 (6617), 26 (4426), 35 (3335) and 53 (2253). 108 is the hyperfactorial of 3 since 108= 1 1 ⋅ 2 2 ⋅ 3 3 {\displaystyle 1^{1}\cdot 2^{2}\cdot

108 (number)

108_(number)

10,000,000

Natural number

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 87,528

10,000,000

Glaisher–Kinkelin constant

Mathematical constant

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

Glaisher–Kinkelin constant

Glaisher–Kinkelin_constant

List of factorial and binomial topics

distribution Gamma function Gaussian binomial coefficient Gould's sequence Hyperfactorial Hypergeometric distribution Hypergeometric function identities Hypergeometric

List of factorial and binomial topics

List_of_factorial_and_binomial_topics

Superfactorial

Product of consecutive factorial numbers

{(n!)^{n+1}}{H(n)}}\end{aligned}}} where H {\displaystyle H} is the hyperfactorial. Following the usual convention for the empty product, the superfactorial

Superfactorial

114 (number)

Natural number

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

114 (number)

114_(number)

Hermite polynomials

Polynomial sequence

e^{-t^{2}/2+ixt}\,dt.\end{aligned}}} The discriminant is expressed as a hyperfactorial: Disc ⁡ ( H n ) = 2 3 2 n ( n − 1 ) ∏ j = 1 n j j Disc ⁡ ( He n ) =

Hermite polynomials

Hermite_polynomials

Exponential factorial

Recursive mathematical formula

factorials grow much more quickly than regular factorials or even hyperfactorials, in fact exhibiting growth equivalent to tetration (in the sense that

Exponential factorial

Exponential_factorial