What is the gamma function in python :
_gamma() _function is defined in Python Math module. It takes one argument and calculates the gamma value for that argument. The gamma function is defined as below :
gamma(x) = factorial(x - 1)
That means the gamma of a number is equal to the factorial of number - 1.
Syntax of gamma function :
The syntax of the gamma function is as below :
Math.gamma(x)
Where, _x _is the number we are calculating the gamma value. This number should be always positive. If it is negative, it will throw one ValueError. If the argument is not a number, it will throw one TypeError. Note that gamma() will return one output if the argument is positive or even negative decimal.
Example of gamma :
Let’s try to check this function with different examples :
import math
print("Gamma for 5 is : {}".format(math.gamma(5)))
print("Gamma for 2.5 is : {}".format(math.gamma(2.5)))
print("Gamma for -8.3 is : {}".format(math.gamma(-8.3)))
It will print the below output :
Gamma for 5 is : 24.0
Gamma for 2.5 is : 1.3293403881791372
Gamma for -8.3 is : -5.040817747151161e-05
Now let’s try to compare gamma with its equivalent factorial for different numbers :
import math
print("Gamma for 5 is : {}".format(math.gamma(5)))
print("Factorial for 4 is : {}".format(math.factorial(4)))
print("----------------")
print("Gamma for 18 is : {}".format(math.gamma(18)))
print("Factorial for 17 is : {}".format(math.factorial(17)))
print("----------------")
print("Gamma for 15 is : {}".format(math.gamma(15)))
print("Factorial for 14 is : {}".format(math.factorial(14)))
print("----------------")
print("Gamma for 10 is : {}".format(math.gamma(10)))
print("Factorial for 9 is : {}".format(math.factorial(9)))
It will print :
Gamma for 5 is : 24.0
Factorial for 4 is : 24
----------------
Gamma for 18 is : 355687428096000.0
Factorial for 17 is : 355687428096000
----------------
Gamma for 15 is : 87178291200.0
Factorial for 14 is : 87178291200
----------------
Gamma for 10 is : 362880.0
Factorial for 9 is : 362880
As you can see that the gamma of a number is equal to the factorial(number - 1).
You can also download the above examples from here