Multiply one Laguerre series to another in Python

To multiply one Laguerre series to another, use the polynomial.laguerre.lagmul() method in Python NumPy. This function returns the multiplication of two Laguerre series c1 * c2. The sequences of coefficients are 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.laguerre.lagmul(c1, c2)

Parameters

The parameters c1 and c2 are 1-D arrays of Laguerre series coefficients ordered from low to high degree.

Example

Let's multiply two Laguerre series step by step ?

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)

# To multiply one Laguerre series to another, use the polynomial.laguerre.lagmul() method
print("\nResult (multiply)....\n", L.lagmul(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 (multiply)....
 [ 10.   4.  16. -12.  18.]

Understanding the Result

The resulting array [ 10. 4. 16. -12. 18.] represents the coefficients of the multiplied Laguerre series. The degree of the result is the sum of the degrees of the input series (in this case, 2 + 2 = 4), giving us 5 coefficients.

Conclusion

The lagmul() function efficiently multiplies two Laguerre series by their coefficient arrays. The result contains coefficients ordered from lowest to highest degree terms.