Convert a Legendre series to a polynomial in Python

To convert a Legendre series to a polynomial, use the laguerre.leg2poly() method in Python Numpy

# Convert an array representing the coefficients of a Legendre series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree.

# The method returns a 1-D array containing the coefficients of the equivalent polynomial ordered from lowest order term to highest. # The parameter c, is a 1-D array containing the Legendre series coefficients, ordered from lowest order term to highest.

Steps

At first, import the required library −

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

Create an array using the numpy.array() method −

c = np.array([1, 2, 3, 4, 5])

Display the array −

print("Our 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 convert a Legendre series to a polynomial, use the laguerre.leg2poly() method in Python Numpy. Convert an array representing the coefficients of a Legendre series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the “standard” basis) ordered from lowest to highest degree −

print("\nResult (legendre to polynomial)...\n",L.leg2poly(c))

Example

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

# Create an array using the numpy.array() method
c = np.array([1, 2, 3, 4, 5])

# Display the array
print("Our 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 convert a Legendre series to a polynomial, use the laguerre.leg2poly() method in Python Numpy
print("\nResult (legendre to polynomial)...\n",L.leg2poly(c))

Output

Our Array...
   [1 2 3 4 5]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(5,)

Result (legendre to polynomial)...
   [ 1.375 -4. -14.25 10. 21.875]