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Python math.erf() Method

The Python math.erf() method is used to calculate the error method. It is a mathematical method that describes the probability of an event occurring within a certain range of values in a normal distribution.

Mathematically, the error method is defined as −

$$\mathrm{erf(x)\:=\:\frac{2}{\sqrt{\pi}}\:\int^{x}_{0}\:e^{−t^{2}}\:dt}$$

Where, e is the base of the natural logarithm and π is the mathematical constant pi. The error method is an odd method, meaning that erf(-x) = -erf(x) and is being bounded between -1 and 1.

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

math.erf(x)

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

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

In the following example, we are calculating the error method for a positive real number using the math.erf() method −

import math
x = 1.5
result = math.erf(x)
print("Error method for x =", x, ":", result)

The output obtained is as follows −

Error method for x = 1.5 : 0.9661051464753108

In here, we are calculating the error method for a negative real number using the math.erf() method −

import math
x = -0.75
result = math.erf(x)
print("Error method for x =", x, ":", result)

Following is the output of the above code −

Error method for x = -0.75 : -0.7111556336535151

In this example, we are evaluating the sum of error methods for x=2 and x/2 using the math.erf() method−

import math
x = 2
result = math.erf(x) + math.erf(x/2)
print("Error method expression result for x =", x, ":", result) 

We get the output as shown below −

Error method expression result for x = 2 : 1.8380230579686676

Now, we use the math.erf() method to directly calculate the error method for x=0 −

import math
x = 0
result = math.erf(x)
print("Error method for x =", x, ":", result)

The result produced is as shown below −

Error method for x = 0 : 0.0

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