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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
  • 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
  • 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
  • Can the factorial function be written as a sum?
    In this paper we give an additive representation of the factorial, which can be proven by a simple quick analytical argument We also present some generalizations, which are linked, on the one hand to an arithmetical theorem proven by Euler (decomposition of primes as the sum of two squares), and, on the other hand, to modern combinatorics
  • Factorial number of digits - Mathematics Stack Exchange
    This is a slightly more accurate approximation that Sterling's approximation, given that you wanted to take the factorial of a relatively small number like 20 We can express this alternatively as, $$\log_{10} n! \approx n \log_{10} n - 0 434 n + \log_{10} (2 \pi n)$$





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