How to add Euler Mascheroni Constant to Each Element of a NumPy Array ?

The Euler-Mascheroni constant ($\gamma$) is a mathematical constant approximately equal to $0.57721$. It frequently appears in number theory, calculus, and mathematical analysis. If you’re working with numerical computations in Python using NumPy, you may encounter situations where you need to add this constant to every element of an array. It represents the limiting difference between the harmonic series and the natural logarithm and appears frequently in integral evaluations, series expansions, and special functions.

Below is a simple example that demonstrates how to create a NumPy array, add the Euler-Mascheroni constant to each of its elements, and print the modified array.

 

Input

#
#Note: if there is an numpy error then install it using pip!
#
import numpy as np  
# Define the Euler-Mascheroni constant
euler_mascheroni_constant = 0.57721

# Create a sample NumPy array
array = np.array([1, 2, 3, 4, 5])

# Add the Euler-Mascheroni constant to each element
result = array + euler_mascheroni_constant

# Display the result
print(array)
print(result)
#

Output

#
[1 2 3 4 5]
[1.57721 2.57721 3.57721 4.57721 5.57721]
#

Explanation

Here, the array  [10,20,30,40,50]  is augmented with the constant $0.57721$, demonstrating how NumPy’s broadcasting feature applies the addition operation to each element of the array without requiring explicit loops.

Why use Numpy ?

NumPy makes this task straightforward thanks to its powerful broadcasting feature, which allows operations between arrays and scalars to be performed effortlessly. The technique is not only efficient but also intuitive, making it ideal for data manipulation in scientific and mathematical projects.

Broadcasting is a powerful feature that allows NumPy to perform element-wise operations between arrays of different shapes or between arrays and scalars without explicit looping, improving both readability and efficiency.

• Efficient multi-dimensional array processing
• Built-in mathematical functions
• Compatibility with various scientific libraries

Advanced Example: Adding the Constant to a 2D Array with Conditional Operations

In this expert-level example, we’ll work with a two-dimensional array. We’ll add the Euler-Mascheroni constant ($\gamma$) only to elements greater than a specified threshold (e.g., 15).

Input

#import numpy as np

# Step 1: Define the Euler-Mascheroni constant
gamma = 0.57721

# Step 2: Create a 2D NumPy array
expert_array = np.array([[10, 20, 30], [5, 15, 25]])

# Step 3: Add the constant conditionally (only to elements > 15)
result = np.where(expert_array > 15, expert_array + gamma, expert_array)

# Step 4: Print the results
print(expert_array)
print("\n")
print(result)
#

 

Output

#
[[10 20 30]
 [ 5 15 25]]

[[10.      20.57721 30.57721]
 [ 5.      15.      25.57721]]
#

Explanation

In this example, we use NumPy’s library np.where function to add the constant conditionally. This ensures the operation only applies to elements greater than 15, showcasing a more advanced and practical use of array manipulation.