Add one Laguerre series to another in Python

To add one Laguerre series to another, use the polynomial.laguerre.lagadd() method in Python NumPy. The method returns an array representing the Laguerre series of their sum.

The function performs element-wise addition of Laguerre series coefficients. 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. The parameters c1 and c2 are 1-D arrays of Laguerre series coefficients ordered from low to high.

Syntax

numpy.polynomial.laguerre.lagadd(c1, c2)

Parameters:

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

Returns: Array representing the Laguerre series of their sum

Example

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

import numpy as np
from numpy.polynomial import laguerre as L

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

# Display the arrays of coefficients
print("Array1...\n", c1)
print("\nArray2...\n", c2)

# Display the datatype
print("\nArray1 datatype...\n", c1.dtype)
print("\nArray2 datatype...\n", c2.dtype)

# Check the Dimensions of both the arrays
print("\nDimensions of Array1...\n", c1.ndim)
print("\nDimensions of Array2...\n", c2.ndim)

# Check the Shape of both the arrays
print("\nShape of Array1...\n", c1.shape)
print("\nShape of Array2...\n", c2.shape)

# Add the two Laguerre series
print("\nResult (sum)....\n", L.lagadd(c1, c2))

Array1...
 [1 2 3]

Array2...
 [3 2 1]

Array1 datatype...
 int64

Array2 datatype...
 int64

Dimensions of Array1...
 1

Dimensions of Array2...
 1

Shape of Array1...
 (3,)

Shape of Array2...
 (3,)

Result (sum)....
 [4. 4. 4.]

Adding Series of Different Lengths

The function can also handle Laguerre series of different lengths ?

import numpy as np
from numpy.polynomial import laguerre as L

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

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

# Add the series
result = L.lagadd(c1, c2)
print("Sum:", result)

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

How It Works

The lagadd() function performs coefficient-wise addition:

• For coefficients at the same position, it adds them directly
• For series of different lengths, missing coefficients are treated as zero
• The result length equals the longer of the two input series

Conclusion

Use numpy.polynomial.laguerre.lagadd() to add Laguerre series by performing element-wise addition of their coefficients. The function handles series of different lengths automatically by treating missing coefficients as zero.