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factorial    
a. 代理店的,阶乘的
n. 阶乘

代理店的,阶乘的阶乘

factorial
阶乘

factorial
阶乘

factorial
adj 1: of or relating to factorials
n 1: the product of all the integers up to and including a given
integer; "1, 2, 6, 24, and 120 are factorials"

Factorial \Fac*to"ri*al\, a.
1. Of or pertaining to a factory. --Buchanan.
[1913 Webster]

2. (Math.) Related to factorials.
[1913 Webster]


Factorial \Fac*to"ri*al\, n. (Math.)
(a) pl. A name given to the factors of a continued product
when the former are derivable from one and the same
function F(x) by successively imparting a constant
increment or decrement h to the independent variable.
Thus the product F(x).F(x h).F(x 2h) . . . F[x
(n-1)h] is called a factorial term, and its several
factors take the name of factorials. --Brande & C.
(b) The product of the consecutive whole numbers from
unity up to any given number; thus, 5 factorial is the
product of 5 times four times three times two times
one, or 120.
[1913 Webster PJC]

The mathematical {function} that takes a
{natural number}, N, and returns the product of N and all
smaller positive integers. This is written

N! = N * (N-1) * (N-2) * ... * 1.

The factorial of zero is one because it is an {empty
product}.

Factorial can be defined {recursively} as

0! = 1
N! = N * (N-1)! , N > 0

The {gamma function} is the equivalent for {real numbers}.

(2005-01-07)

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  • Factorial, but with addition - Mathematics Stack Exchange
    Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious But I'm wondering what I'd need to use to describe $$5+4+3+2+1$$ like the factorial $5!$ way EDIT: I know about the formula I want to know if there's a short notation
  • factorial - Why does 0! = 1? - Mathematics Stack Exchange
    $\begingroup$ The theorem that $\binom{n}{k} = \frac{n!}{k!(n-k)!}$ already assumes $0!$ is defined to be $1$ $ Otherwise this would be restricted to $0 <k
  • What does the factorial of a negative number signify?
    For example: the factorial of zero i e an empty set ( doesn't occur) is 1 As the empty set can be arranged only in 1 way - i e by filling nothing Now, let's take an example: 5 distinct seats How many ways 5 distinct seats can be arranged? - 5! ways i e 120 So, basically, factorial gives us the arrangements
  • Defining the factorial of a real number - Mathematics Stack Exchange
    $\begingroup$ Some theorems that suggest that the Gamma Function is the "right" extension of the factorial to the complex plane are the Bohr–Mollerup theorem and the Wielandt theorem $\endgroup$ – kuzzooroo





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