Convert a polynomial to Hermite_e series in Python

To convert a polynomial to a Hermite_e series, use the hermite_e.poly2herme() method in Python NumPy. This function converts an array representing polynomial coefficients (ordered from lowest to highest degree) to an array of coefficients for the equivalent Hermite_e series.

Syntax

numpy.polynomial.hermite_e.poly2herme(pol)

Parameters

The pol parameter is a 1-D array containing the polynomial coefficients ordered from lowest degree to highest degree.

Example

Let's convert a polynomial with coefficients [1, 2, 3, 4, 5] to its equivalent Hermite_e series ?

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

# Create an array representing polynomial coefficients
coeffs = np.array([1, 2, 3, 4, 5])

# Display the polynomial coefficients
print("Polynomial coefficients:", coeffs)
print("Dimensions:", coeffs.ndim)
print("Shape:", coeffs.shape)
print("Datatype:", coeffs.dtype)

# Convert polynomial to Hermite_e series
hermite_coeffs = H.poly2herme(coeffs)
print("\nHermite_e series coefficients:", hermite_coeffs)

Polynomial coefficients: [1 2 3 4 5]
Dimensions: 1
Shape: (5,)
Datatype: int64

Hermite_e series coefficients: [19. 14. 33.  4.  5.]

How It Works

The polynomial 1 + 2x + 3x² + 4x³ + 5x? is converted to its equivalent representation using Hermite_e polynomials. The resulting coefficients [19, 14, 33, 4, 5] represent the same mathematical function expressed in the Hermite_e basis.

Conclusion

The hermite_e.poly2herme() method efficiently converts polynomial coefficients to their Hermite_e series representation. This conversion is useful in numerical analysis and mathematical computations involving orthogonal polynomials.