# Integrate a Hermite series and multiply the result by a scalar before the integration constant is added using NumPy in Python

• Last Updated : 03 Jun, 2022

In this article, we will see how to integrate a Hermite series and multiply the result by a scalar before the integration constant is added in Python.

## hermite.hermint method

Hermite nodes are utilised as matching points for optimising polynomial interpolation, Hermite polynomials are important in approximation theory. NumPy has a function called hermite.hermint() that can be used to integrate the Hermite series in a specific order. It will require two parameters: c, which is an array, and scl, which is a scalar that will be multiplied by the integrated Hermite series before the integration constant is added.

Syntax: hermite.hermint(c,scl)

Parameter:

• c: an array
• scl: A scalar value

Return: Hermite series coefficients of the integral.

### Example 1

In this example, we will create a one-dimensional NumPy coefficient array with 6 elements and integrate the Hermite series and multiply the result by a scalar with the value -2  before the integration constant.

## Python3

 `# import the numpy module``import` `numpy`` ` `# import hermite``from` `numpy.polynomial ``import` `hermite`` ` `# Create an array of hermite series``# coefficients with 6 elements``coefficient_array ``=` `numpy.array([``1``, ``2``, ``3``, ``4``, ``3``, ``5``])`` ` `# display array``print``(``"Coefficient array: "``, coefficient_array)`` ` `# display the dimensions``print``(``"Dimensions: "``, coefficient_array.ndim)`` ` `# integrate hermite series with scale=2``print``(    hermite.hermint(coefficient_array, scl``=``-``2``))`

Output:

Coefficient array:  [1 2 3 4 3 5]

Dimensions:  1

[-90.          -1.          -1.          -1.          -1.

-0.6         -0.83333333]

### Example 2

In this example, we will create a two-dimensional NumPy coefficient array with 6 elements each and integrate the Hermite series and multiply the result by a scalar with value -1 before the integration constant.

## Python3

 `# import the numpy module``import` `numpy`` ` `# import hermite``from` `numpy.polynomial ``import` `hermite`` ` `# Create an 2d array of hermite series``# coefficients with 6 elements each``coefficient_array ``=` `numpy.array([[``1``, ``2``, ``3``, ``4``, ``3``, ``5``], ``                                 ``[``4``, ``5``, ``6``, ``4``, ``3``, ``2``]])`` ` `# display array``print``(``"Coefficient array: "``, coefficient_array)`` ` `# display the dimensions``print``(``"Dimensions: "``, coefficient_array.ndim)`` ` `# integrate hermite series with scale=-1``print``(    hermite.hermint(coefficient_array, scl``=``-``1``))`

Output:

```Coefficient array:  [[1 2 3 4 3 5]
[4 5 6 4 3 2]]
Dimensions:  2
[[-2.   -2.5  -3.   -2.   -1.5  -1.  ]
[-0.5  -1.   -1.5  -2.   -1.5  -2.5 ]
[-1.   -1.25 -1.5  -1.   -0.75 -0.5 ]]```

My Personal Notes arrow_drop_up