Factorial factor is an operation symbol invented by Keyston Kramp (1760 ~1826) in 1808, and it is a mathematical term.

The factorial of a positive integer is the product of all positive integers less than or equal to this number, and the factorial of 0 is 1. The factorial writing of natural number n! . In 1808, Keyston Kaman introduced this symbol.

Which is n! =1× 2× 3× ...× n. The factor can also be defined recursively: 0! = 1，n！ =(n- 1)！ ×n .

Extended data:

With "m! ! "Express delivery.

When m is a natural number, it means the product of all positive integers not exceeding m and having the same parity with m, such as:

When m is a negative odd number, it means the reciprocal of the absolute product of all negative odd numbers whose absolute values are less than their absolute values.

When m is a negative even number, m! ! Does not exist.

N factorial representation of any natural number greater than or equal to 1;

Extending factorial to pure complex number;

Positive real factorial: n! =│n│！ =n(n- 1)(n-2)....( 1+x)。 x！ =(i^4m).│n│！

Negative real factorial: (-n)! =cos(mπ)│n│！ =(i^2m)..(n- 1)(n-2)....( 1+x)。 x！

(Ni)! =(i^m)│n│！ =(i^m)..(n- 1)(n-2)....( 1+x)。 x！

(-ni)！ =(i^3m)│n│！ =(i^3m)..(n- 1)(n-2)....( 1+x)。 x！

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