We have been taught our whole lives that only positive integers have factorials.
But is this true.....?
The answer is NO. Factorials for decimals do exist!
The formula to calculate factorials that we all have learnt is :
n(n-1)(n-2)....2*1 or
(n-1)! = n!/n
I am about to introduce a new function: The Gamma Function.
The Gamma Function :
The (complete) Gamma Function is defined to be an extension of the factorial to complex and real number arguments.
The gamma function can be defined as a definite integral for R[z] (Euler's integral form).
The graph for the Gamma Function:
To find the factorial of a decimal(n):
Plug the value of (n+1) in the Gamma Function shown above.
If you know how to solve it yourself, great!.
If you do not, you can put in the integral into https://www.integral-calculator.com/ and find the Answers.
A few examples :
fact(0.5) fact(4.82)
0.5!= ∫ e^-x * x^.5 dx 4.82! = ∫ e^-x * x^3.82 dx
0.5!= √π / 2 = 0.886226(approx) 4.82! = 18.36756(approx)
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