Multiply one Hermite_e series to another in Python

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

Syntax

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

Parameters

The parameters are 1-D arrays of Hermite_e series coefficients ordered from low to high ?

• c1, c2 ? 1-D arrays of Hermite_e polynomial coefficients

Example

Let's multiply two Hermite_e series using coefficient arrays ?

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])

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

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

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

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

# Multiply the Hermite_e series
print("\nResult (multiply)....")
print(H.hermemul(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)....
[13. 24. 26.  8.  3.]

How It Works

The hermemul() function multiplies two Hermite_e polynomial series by convolving their coefficient arrays. The resulting array has a degree equal to the sum of the degrees of the input polynomials.

Conclusion

Use numpy.polynomial.hermite_e.hermemul() to multiply Hermite_e polynomial series. The function takes two 1-D coefficient arrays and returns their polynomial product as a new coefficient array.