Differentiate a Legendre series and set the derivatives in Python

To differentiate a Legendre series, use the polynomial.laguerre.legder() method in Python. Returns the Legendre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl. The 1st parameter, c is an array of Legendre series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index.

The 2nd parameter, m is the number of derivatives taken, must be non-negative. (Default: 1). The 3rd parameter, scl is a scalar. Each differentiation is multiplied by scl. The end result is multiplication by scl**m. This is for use in a linear change of variable. (Default: 1). The 4th parameter, axis is an Axis over which the derivative is taken. (Default: 0).

Steps

At first, import the required library −

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

Create an array of coefficients −

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

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 differentiate a Legendre series, use the polynomial.laguerre.legder() method in Python. Returns the Legendre series coefficients c differentiated m times along axis. At each iteration the result is multiplied by scl −

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

Example

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

# Create an array of coefficients
c = np.array([1,2,3,4])

# 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 differentiate a Legendre series, use the polynomial.laguerre.legder() method in Python
print("\nResult...\n",L.legder(c, 3))

Output

Our Array...
   [1 2 3 4]

Dimensions of our Array...
1

Datatype of our Array object...
int64

Shape of our Array object...
(4,)

Result...
   [60.]