How to find the factorial of fractional numbers using matlab code?

Question

Athira T Das 2022-7-16

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1761720-how-to-find-the-factorial-of-fractional-numbers-using-matlab-code

评论： Steven Lord 2022-7-18

I have an array s1. I want to evaluate the factorial of s1.

M=3;
m1 = 0:M;
s1 = m1./2
s1 = 1×4
         0    0.5000    1.0000    1.5000
factorial(s1)
Error using factorial
N must be an array of real non-negative integers.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

John D'Errico 2022-7-16

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1761720-how-to-find-the-factorial-of-fractional-numbers-using-matlab-code#answer_1008950

在 MATLAB Online 中打开

You CANNOT compute the factorial of a fractional number. Factorials are defined only for integers.

HOWEVER...

It is true that

factorial(N) == gammma(N+1)

for integer N. You might think of the gamma function as an extension of the factorial function onto the real line. For example:

N = 0:10;
factorial(N)
ans = 1×11
           1           1           2           6          24         120         720        5040       40320      362880     3628800
gamma(N + 1)
ans = 1×11
           1           1           2           6          24         120         720        5040       40320      362880     3628800

And the gamma function is defined on the real line. So...

gamma(1.5)
ans = 0.8862

is thus what you might think of when you write (0.5)!.

fplot(@gamma,[.1,5])

In fact, the gamma function follows the smiple rules that work for factorial. Thus we would see that if

factorial(N) == N*factorial(N-1)

then we might hope it would be true that

gamma(N+1) = N*gamma(N)

For example, we can test that as:

format long g
[gamma(3.25)*3.25,gamma(4.25)]
ans = 1×2
          8.28508514183522          8.28508514183522

So the gamma function follows a similar recursive rule like the factorial function. The only differnce is you don't have any easy way to start the recursion.