“factorial”的概念、定义、翻译、参考文献-科学参考

factorial

Physics

The product of a given number and all the whole numbers below it. It is usually written n!, e.g. factorial 4=4!=4×3×2×1=24. Factorial 0 is defined as 1.

Mathematics

For a positive integer n, the notation n! (read as ‘n factorial’ or ‘n shriek’) is used for the product n(n−1)(n−2)…×2×1. Thus 4!=4×3×2×1=24. Also, by definition, 0!=1. See also gamma function.

For a positive integer n, the ‘double factorial’ notation n!! denotes the products

$\begin{array}{l} n \times (n - 2) \times (n - 4) \times \dots \times 1 = \frac{(2 k)!}{2^{k} k!} \\ when n = 2 k - 1; \\ n \times (n - 2) \times (n - 4) \times \dots \times 2 = 2^{k} k! when n = 2 k . \end{array}$

Statistics

If n is a positive integer, then factorial n, written as n!, is defined by $factorial$ with 0! defined to be 1. The notation was introduced in about 1810 by the French mathematician Christian Kramp (1760–1826). Factorial n is the number of different orderings of n individuals. The numerical value of n! increases rapidly with n: $factorial$
For n>1, successive values of n! can be calculated using $factorial$ If n is not an integer, factorial n can be defined via the gamma function Γ as $factorial$ For large values of n an approximation is provided by Stirling's formula.

Chemical Engineering

The product of all the positive whole integers being considered. Note that 0! has a value of 1. For example, 5! is 0 × 1 × 2 × 3 × 4 × 5 = 20.

单词	factorial
释义	factorial Physics The product of a given number and all the whole numbers below it. It is usually written n!, e.g. factorial 4=4!=4×3×2×1=24. Factorial 0 is defined as 1. Mathematics For a positive integer n, the notation n! (read as ‘n factorial’ or ‘n shriek’) is used for the product n(n−1)(n−2)…×2×1. Thus 4!=4×3×2×1=24. Also, by definition, 0!=1. See also gamma function. For a positive integer n, the ‘double factorial’ notation n!! denotes the products $\begin{array}{l} n \times (n - 2) \times (n - 4) \times \dots \times 1 = \frac{(2 k)!}{2^{k} k!} \\ when n = 2 k - 1; \\ n \times (n - 2) \times (n - 4) \times \dots \times 2 = 2^{k} k! when n = 2 k . \end{array}$ Statistics If n is a positive integer, then factorial n, written as n!, is defined by $factorial$ with 0! defined to be 1. The notation was introduced in about 1810 by the French mathematician Christian Kramp (1760–1826). Factorial n is the number of different orderings of n individuals. The numerical value of n! increases rapidly with n: $factorial$ For n>1, successive values of n! can be calculated using $factorial$ If n is not an integer, factorial n can be defined via the gamma function Γ as $factorial$ For large values of n an approximation is provided by Stirling's formula. Chemical Engineering The product of all the positive whole integers being considered. Note that 0! has a value of 1. For example, 5! is 0 × 1 × 2 × 3 × 4 × 5 = 20.
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