- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Integrate a Legendre series and set the lower bound of the integral in Python

To integrate a Legendre series, use the polynomial.legendre.legint() method in Python. The method returns the Legendre series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The scaling factor is for use in a linear change of variable.

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 an order of integration, must be positive. (Default: 1). The 3rd parameter, k is an integration constant(s). The value of the first integral at lbnd is the first value in the list, the value of the second integral at lbnd is the second value, etc. If k == [] (the default), all constants are set to zero. If m == 1, a single scalar can be given instead of a list.

The 4th parameter, lbnd is the lower bound of the integral. The 5th parameter, scl is a scalar. Following each integration the result is multiplied by scl before the integration constant is added. (Default: 1). The 6th parameter, axis is an Axis over which the integral 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])

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 integrate a Legendre series, use the polynomial.legendre.legint() method in Python. The method returns the Legendre series coefficients c integrated m times from lbnd along axis. At each iteration the resulting series is multiplied by scl and an integration constant, k, is added. The scaling factor is for use in a linear change of variable −

print("\nResult...\n",L.legint(c, lbnd = -2))

## Example

import numpy as np from numpy.polynomial import legendre as L # Create an array of coefficients c = np.array([1,2,3]) # 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 integrate a Legendre series, use the polynomial.legendre.legint() method in Pytho print("\nResult...\n",L.legint(c, lbnd = -2))

## Output

Our Array... [1 2 3] Dimensions of our Array... 1 Datatype of our Array object... int64 Shape of our Array object... (3,) Result... [7.33333333 0.4 0.66666667 0.6 ]

- Related Articles
- Integrate a Laguerre series and set the lower bound of the integral in Python
- Integrate a Hermite series and set the lower bound of the integral in Python
- Integrate a Chebyshev series and set the lower bound of the integral in Python
- Integrate a Hermite_e series and set the lower bound of the integral in Python
- Integrate a polynomial and set the lower bound of the integral in Python
- Integrate a Legendre series and set the order of integration in Python
- Integrate a Legendre series and set the integration constant in Python
- Integrate a Legendre series in Python
- Integrate a Legendre series over specific axis in Python
- Integrate a Legendre series over axis 1 in Python
- Integrate a Legendre series over axis 0 in Python
- Differentiate a Legendre series and set the derivatives in Python
- Integrate a Laguerre series and set the order of integration in Python
- Integrate a Hermite series and set the order of integration in Python
- Integrate a Chebyshev series and set the order of integration in Python