Math 10! What do you mean?

10! Represents the factorial of 10.

The concept of factorial

Factorial factor is an operation symbol invented by Keyston Kramp (1760–1826) in 1808.

Factorial factor is also a term in mathematics.

Factorial calculation method

Factorial factor refers to the required number obtained by multiplying 1 by 2 times 3 times 4.

For example, if the required number is 4, the factorial formula is 1×2×3×4, and the product is 24, that is, the factorial of 4. For example, if the required number is 6, the factorial formula is 1× 2× 3×…× 6, and the product is 720, which is the factorial of 6. For example, if the required number is n, the factorial formula is 1× 2× 3× …× n, and the product obtained is X, that is, the factorial of n. ..

Representation of factorial

When expressing factorial, use "!" To show. Such as the factorial of x, it is expressed as x!

[Edit this paragraph]

Factorial of numbers within 20

Because the product is very large, the factor is usually difficult to calculate.

The factorials from 0 to 20 are listed below:

0! = 1,

1! = 1,

2! =2,

3! =6,

4! =24,

5! = 120,

6! =720,

7! =5040,

8! =40320

9! =362880

10! =3628800

1 1! =399 16800

12! =47900 1600

13! =6227020800

14! =87 17829 1200

15! = 1307674368000

16! =20922789888000

17! =355687428096000

18! =6402373705728000

19! = 12 1645 100408832000

20! =2432902008 176640000

In addition, mathematicians define 0! = 1, so 0! = 1!

Definition range of factorial

Usually, the factorial is defined in the range of natural numbers, and there is no factorial for decimals, like 0.5! ,0.65! ,0.777! It's all wrong But sometimes we define the Gamma function as the factorial of non-integers, because when x is a positive integer n, the value of the Gamma function is the factorial of n- 1

Gamma function (gamma function)

γ (x) = ∫ e (-t) * t (x- 1) dt (the lower integral limit is zero and the upper integral limit is +∞) (x >; 0,- 1,-2,-3,……)

Using the knowledge of integral, we can prove that γ (x) = (x- 1) * γ (x- 1).

Therefore, when x is an integer n, γ (n) = (n-1) (n-2) ... = (n-1)!

So the gamma function actually extends the factorial.

[Computer Science]

Find the factorial of 365 with Ruby.

def ask factorial(num)factorial = 1；

1.step(num, 1){|i| factorial *=i}

return factorial end factorial = ask factorial(365)

Release factorial

Formula related to factorial