Generate a Hermite_e series with given roots using NumPy in Python

In this article, we will cover how to raise a Hermite_e series to power in Python using NumPy.

hermite_e.hermefromroots() function

We use the hermite_e.hermefromroots() function present in the NumPy module of python to construct a Hermite_e series with the given roots. A 1-D array of coefficients is returned by the following function. we will get a real array if all of the roots are real; if any of the roots are complex than we will get a complex array even if all of the coefficients in the result are real. 

Syntax: numpy.polynomial.hermite_e.hermefromroots(roots)

Parameters: 

• Sequence containing the roots.

Returns : ndarray ,1-D array of coefficients. If all roots are real then out is a real array, if some of the roots are complex, then out is complex 

Steps to generate the Hermite_e series with given roots : 

Step 1: Importing the hermite_e library.

from numpy.polynomial import hermite_e

Step 2: Create a 1-dimensional array of roots.

arr = [1,2,0]

Step 3: Finally generate a Hermite_e  series with the array of roots.

print(hermite_e.hermefromroots(arr))

Example 1:

In this example, we are creating a simple array to return a Hermite_e series with the given roots using hermefromroots.

# import hermite_e library
from numpy.polynomial import hermite_e

# create an array 'arr' of roots
arr = [1, 0, -2]

# generate a Hermite_e series with given 
# roots using hermefromroots() function
print(hermite_e.hermefromroots(arr))

Output:

[1. 1. 1. 1.] 

Example 2:

In this example, we are creating an array with the complex number to return a Hermite_e series with the given complex roots using hermefromroots.

# import hermite_e library
from numpy.polynomial import hermite_e

# generate a Hermite_e series with given
# roots using hermefromroots() function
print(hermite_e.hermefromroots((-2, 4, 5, 4+5j)))

Output:

[-127.-165.j   -1. -25.j   36. +35.j  -11.  -5.j    1.  +0.j]

Example 3:

In this example, we are creating a NumPy array of 8 elements and returning the Hermite_e series with the given roots using hermefromroots.

# import hermite_e library
from numpy.polynomial import hermite_e
import numpy

# create an array 'arr' of roots
arr = numpy.array([1, 2, 3, 4, 5, 6, 7, 8])

# generate a Hermite_e series with given 
# roots using hermefromroots() function
print(hermite_e.hermefromroots(arr))

Output:

[ 2.34086e+05 -3.83256e+05  2.77808e+05 -1.16424e+05  3.08490e+04

 -5.29200e+03  5.74000e+02 -3.60000e+01  1.00000e+00]