Raise a Legendre series to a power in Python

To raise a Legendre series to a power, use the polynomial.legendre.legpow() method in Python Numpy. The method returns the Legendre 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 P_0 + 2*P_1 + 3*P_2. Returns the Legendre 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 P_0 + 2*P_1 + 3*P_2.

The parameter, c is a 1-D array of Legendre series coefficients ordered from low to high. The parameter, pow 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 library −

import numpy as np
from numpy.polynomial import laguerre as L

Create 1-D arrays of Laguerre series coefficients −

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 Legendre series to a power, use the polynomial.legendre.legpow() method in Python Numpy −

print("\nResult....\n",L.legpow(c, 3))

Example

import numpy as np
from numpy.polynomial import legendre as L

# Create 1-D arrays of Laguerre series coefficients
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 Legendre series to a power, use the polynomial.legendre.legpow() method in Python Numpy
# The method returns the Legendre 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 P_0 + 2*P_1 + 3*P_2.
print("\nResult....\n",L.legpow(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....
   [16.74285714 42.17142857 55.14285714 46.4 33.8025974 15.42857143 6.31168831]