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Python Program to Integrate a Chebyshev Series and Set the Integration Constant

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  • Last Updated : 21 Apr, 2022

In this article, we will discuss how to integrate a Chebyshev Series and set the integration constant

To perform Chebyshev integration, NumPy provides a function called chebyshev.chebint which can be used to integrate Chebyshev series. 

Syntax: chebyshev.chebint(c, m=1, k=[], lbnd=0, scl=1, axis=0)

Parameters:

  • c – Array of Chebyshev series coefficients.
  • m – (integer) Order of integration, must be positive
  • k –  Integration constant. The value of the first integral at zero is the first value in the list, the value of the second integral at zero is the second value, etc
  • lbnd – The lower bound of the integral. (Default: 0) 
  • scl – Following each integration the result is multiplied by scl before the integration constant is added. (Default: 1)
  • axis – Axis over which the integral is taken.

Example 1:

In the first example. let us consider a 1D array with a first-order integration and 3 as an integration constant. Import the necessary packages as shown and pass the appropriate parameters as shown below.

Python3




import numpy as np
from numpy.polynomial import chebyshev
  
# co.efficient array
c = np.array([11, 12, 13, 14, 15])
  
print(f'The shape of the array is {c.shape}')
print(f'The dimension of the array is {c.ndim}D')
print(f'The datatype of the array is {c.dtype}')
  
res = chebyshev.chebint(c, m=1, k=3)
  
# integrated chebyshev series 
# with integration constant of 1
print(f'Resultant series ---> {res}')

Output:

 

Example 2:

In the second example. let us consider a 2D array with a first-order integration and 5 as an integration constant. Import the necessary packages as shown and pass the appropriate parameters as shown below.

Python3




import numpy as np
from numpy.polynomial import chebyshev
  
# co.efficient array
c = np.array([[11, 12, 13, 14, 15], [3, 4, 5, 6, 7]])
  
print(f'The shape of the array is {c.shape}')
print(f'The dimension of the array is {c.ndim}D')
print(f'The datatype of the array is {c.dtype}')
  
res = chebyshev.chebint(c, m=1, k=5)
  
# integrated chebyshev series
# with integration constant of 5
print(f'Resultant series ---> {res}')

Output:

 

Example 3:

In the third example. let us consider a 3D array with a fifth-order integration and 7 as an integration constant. Import the necessary packages as shown and pass the appropriate parameters as shown below.

Python3




import numpy as np
from numpy.polynomial import chebyshev
  
# co.efficient array
c = np.array([[[11, 12, 13, 14, 15],
               [3, 4, 5, 6, 7],
               [21, 22, 23, 24, 25]]])
  
print(f'The shape of the array is {c.shape}')
print(f'The dimension of the array is {c.ndim}D')
print(f'The datatype of the array is {c.dtype}')
  
res = chebyshev.chebint(c, m=5, k=7)
  
# integrated chebyshev series
# with integration constant of 7
print(f'Resultant series ---> {res}')

Output:

 


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