Python math.gamma() Method

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The Python math.gamma() method calculates the gamma method, denoted as Γ. It is a mathematical extension of the factorial() method to non-integer values. The gamma method is defined for all complex numbers except non-positive integers.

Mathematically, the gamma method is defined as −

$$\mathrm{\Gamma(x)\:=\:\int_{0}^{∞}\:t^{x-1}e^{-t}dt}$$

Where, e is the base of the natural logarithm. The gamma method has various properties, they are as follows −

• It is defined for all complex numbers x except non-positive integers (x ≤ 0).
• For positive integers, Γ(n) = (n-1)!, where n! denotes the factorial of n.
• It is a continuous and differentiable method.
• It satisfies the recurrence relation Γ(x + 1) = x.Γ(x) for all x > 0.
• It grows rapidly as x increases, and approaches infinity as x approaches zero from the right.

Syntax

Following is the basic syntax of the Python math.gamma() method −

math.gamma(x)

Parameters

This method accepts a real number or a numeric expression as a parameter for which you want to calculate the gamma method.

Return Value

The method returns the value of gamma method evaluated at x.

Example 1

In the following example, we are calculating the gamma method for a positive integer using the math.gamma() method −

import math
x = 5
result = math.gamma(x)
print("Gamma method for x =", x, ":", result)

Output

The output obtained is as follows −

Gamma method for x = 5 : 24.0

Example 2

In here, we are calculating the gamma method for a positive real number using the math.gamma() method −

import math
x = 2.5
result = math.gamma(x)
print("Gamma method for x =", x, ":", result)

Output

Following is the output of the above code −

Gamma method for x = 2.5 : 1.3293403881791372

Example 3

In this example, we are evaluating the product of gamma methods for x=3 and x + 1 using the math.gamma() method −

import math
x = 3
result = math.gamma(x) * math.gamma(x+1)
print("Expression result for x =", x, ":", result)

Output

We get the output as shown below −

Expression result for x = 3 : 12.0

Example 4

Now, we use the math.gamma() method to calculate the gamma method for a negative number −

import math
x = -3.5
result = math.gamma(x)
print("Gamma method for x =", x, ":", result)

Output

The result produced is as shown below −

Gamma method for x = -3.5 : 0.27008820585226917