Raise a Hermite_e series to a power in Python

To raise a Hermite_e series to a power, use the polynomial.hermite_e.hermepow() method in Python NumPy. The method returns a Hermite_e series raised to the specified power. The argument c is a sequence of coefficients ordered from low to high, i.e., [1,2,3] represents the series P_0 + 2*P_1 + 3*P_2.

Parameters

The hermepow() method accepts the following parameters ?

• c ? 1-D array of Hermite_e series coefficients ordered from low to high
• pow ? Power to which the series will be raised
• maxpower ? Maximum power allowed (default is 16) to limit series growth

Example

Let's create a Hermite_e series and raise it to the power of 3 ?

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

# Create 1-D array of Hermite_e series coefficients
c = np.array([1, 2, 3])

# Display the coefficient array
print("Our coefficient Array...")
print(c)

# Check the dimensions
print("\nDimensions of our Array...")
print(c.ndim)

# Get the datatype
print("\nDatatype of our Array object...")
print(c.dtype)

# Get the shape
print("\nShape of our Array object...")
print(c.shape)

# Raise Hermite_e series to power 3
result = H.hermepow(c, 3)
print("\nResult after raising to power 3...")
print(result)

Our coefficient Array...
[1 2 3]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(3,)

Result after raising to power 3...
[ 355.  642. 1119.  476.  387.   54.   27.]

Understanding the Result

The original series [1, 2, 3] represents P_0 + 2*P_1 + 3*P_2. When raised to the power of 3, the resulting coefficients are [355, 642, 1119, 476, 387, 54, 27], representing a higher-degree Hermite_e polynomial.

Conclusion

The hermepow() method efficiently raises Hermite_e series to any specified power. The maxpower parameter helps control computational complexity for large powers.