Add one Hermite_e series to another in Python

To add one Hermite_e series to another, use the polynomial.hermite_e.hermeadd() method in NumPy. The method returns an array representing the Hermite_e series of their sum. The arguments are sequences of coefficients ordered from lowest order term to highest, i.e., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2.

Syntax

numpy.polynomial.hermite_e.hermeadd(c1, c2)

Parameters:

• c1, c2 ? 1-D arrays of Hermite_e series coefficients ordered from low to high

Returns: Array representing the sum of the two Hermite_e series

Example

Let's create two Hermite_e series and add them together ?

import numpy as np
from numpy.polynomial import hermite_e as H

# Create 1-D arrays of Hermite_e series coefficients
c1 = np.array([1, 2, 3])
c2 = np.array([3, 2, 1])

print("First Hermite_e series coefficients:", c1)
print("Second Hermite_e series coefficients:", c2)

# Add the two Hermite_e series
result = H.hermeadd(c1, c2)
print("Sum of the two series:", result)

First Hermite_e series coefficients: [1 2 3]
Second Hermite_e series coefficients: [3 2 1]
Sum of the two series: [4. 4. 4.]

How It Works

The hermeadd() function performs element-wise addition of the coefficients. For series c1 = [1,2,3] and c2 = [3,2,1], the result is [1+3, 2+2, 3+1] = [4, 4, 4].

Different Length Series

The function can also handle series of different lengths ?

import numpy as np
from numpy.polynomial import hermite_e as H

# Series of different lengths
c1 = np.array([1, 2])
c2 = np.array([3, 2, 1, 4])

print("First series:", c1)
print("Second series:", c2)

result = H.hermeadd(c1, c2)
print("Sum:", result)

First series: [1 2]
Second series: [3 2 1 4]
Sum: [4. 4. 1. 4.]

Conclusion

Use numpy.polynomial.hermite_e.hermeadd() to add two Hermite_e series by performing element-wise addition of their coefficients. The function automatically handles series of different lengths by padding shorter series with zeros.