Raise a Chebyshev series to a power in Python

To raise a Chebyshev series to a power, use the chebyshev.chebpow() method in Python Numpy. Returns the Chebyshev series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series T_0 + 2*T_1 + 3*T_2. The method returns the Chebyshev series of power.

The parameter, c is a 1-D array of Chebyshev series coefficients ordered from low to high. The parameter, power is a power to which the series will be raised. The parameter, maxpower is the maximum power allowed. This is mainly to limit growth of the series to unmanageable size. Default is 16.

Steps

At first, import the required libraries -

import numpy as np
from numpy.polynomial import chebyshev as C

Create 1-D array of Chebyshev series coefficient −

c = np.array([1,2,3])

Display the coefficient array −

print("Our coefficient Array...\n",c)

Check the Dimensions −

print("\nDimensions of our Array...\n",c.ndim)

Get the Datatype −

print("\nDatatype of our Array object...\n",c.dtype)

Get the Shape −

print("\nShape of our Array object...\n",c.shape)

To raise a Chebyshev series to a power, use the chebyshev.chebpow() method in Python Numpy. Returns the Chebyshev series c raised to the power pow. The argument c is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series T_0 + 2*T_1 + 3*T_2 −

print("\nResult...\n",C.chebdiv(c,3))

Example

import numpy as np
from numpy.polynomial import chebyshev as C

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

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

# Check the Dimensions
print("\nDimensions of our Array...\n",c.ndim)

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

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

# To raise a Chebyshev series to a power, use the chebyshev.chebpow() method in Python Numpy
print("\nResult...\n",C.chebdiv(c,3))

Output

Our coefficient Array...
[1 2 3]

Dimensions of our Array...
1

Datatype of our Array object...
int64

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

Result...
(array([0.33333333, 0.66666667, 1. ]), array([0.]))