Integrate a Hermite_e series Over Axis 0 using Numpy in Python

Integrate a Hermite_e series Over Axis 0 using Numpy in Python

If you want to integrate a Hermite_e series over axis 0, you can use the hermeint function provided by the numpy.polynomial.hermite_e module. This function returns the Hermite_e series coefficients of the antiderivative (integral) of a Hermite_e series.

Here's how you can perform the integration:

  1. Define your Hermite_e series coefficients.
  2. Use the hermeint function to get the coefficients of the integral.
  3. If desired, evaluate the integrated polynomial at specific points or over a range.

Let's walk through an example:

import numpy as np # Define your Hermite_e series coefficients # For instance, c = [c_0, c_1, c_2, ...] represents c_0 + c_1*He_1(x) + c_2*He_2(x) + ... coefficients = [1, 2, 3] # This represents 1 + 2*He_1(x) + 3*He_2(x) # Integrate the Hermite_e series over axis 0 integrated_coeffs = np.polynomial.hermite_e.hermeint(coefficients) print("Integrated Coefficients:", integrated_coeffs) # Optional: Evaluate the integrated polynomial at a specific point x_value = 1.5 result = np.polynomial.hermite_e.hermeval(x_value, integrated_coeffs) print(f"Value of the integrated polynomial at x = {x_value}:", result)

In this example, the hermeint function returns the coefficients of the Hermite_e series of the antiderivative. The constant of integration is set to 0 by default, but you can adjust it if necessary.

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