# 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