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Python math.gamma() Method

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.

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

math.gamma(x)

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

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

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)

The output obtained is as follows −

Gamma method for x = 5 : 24.0

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)

Following is the output of the above code −

Gamma method for x = 2.5 : 1.3293403881791372

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)

We get the output as shown below −

Expression result for x = 3 : 12.0

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)

The result produced is as shown below −

Gamma method for x = -3.5 : 0.27008820585226917

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