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Maclaurin's_series_function(1/1-x²) (Python recipe) by Fouad Teniou
ActiveState Code (http://code.activestate.com/recipes/577292/)

C. Maclaurin. A Scottish mathematician gained his master degree at age 17, and his major mathematics' work arise from his special knowledge in Newton's ideas and the formulation of Newton's methods.

However, C. Maclaurin also contributed to the astronomy science and helped to improve maps and invented some mechanical devices .

My mathematics python's programs is a set of Maclaurin's series to compute some of the most important functions in calculus.

Though, the computation of an infinite sum which give the value of a function in terms of the derivatives evaluated at a special case where x0 = 0,in contrast with Taylor series.

Maclaurin's series to approximate f(x) = (1/1-x^2)

Python, 58 lines
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#On the name of ALLAH and may the blessing and peace of Allah 
#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.
#Author : Fouad Teniou
#Date : 06/07/10
#version :2.6

"""
maclaurin_series_two is a function to compute 1/1+x^2 using maclaurin series
and the interval of convergence is -1 < x < 1 
1/1+x^2 = 1 - x^2 + x^4- x^6 ...........
"""

def error_two(number):
    """ Raises interval of convergence error."""
    
    if number >= 1 or number <= -1 :
        raise TypeError,\
            "\n<The interval of convergence should be -1 < value < 1 \n"

def maclaurin_series_two(value, k):
    """
    Compute maclaurin's series approximation for 1/1+x^2
    """
    
    global first_value
    first_value = 0.0
    
    #attempt to Approximate 1/1+x^2 for a given value
    try:
        error_two(value)
        for item in xrange(0,k,4):
            next_value = value**item
            first_value += next_value
            
        for item in xrange(2,k,4):
            next_value = -1*(value**item)
            first_value += next_value
            
        return first_value
    
    #Raise TypeError if input is not within the interval of convergence
    except TypeError, exception:
        print exception 

if __name__ == "__main__":

   maclaurin_series1 = maclaurin_series_two(0.1,100)
   print maclaurin_series1
   maclaurin_series2 = maclaurin_series_two(0.3,100)
   print maclaurin_series2
   maclaurin_series3 = maclaurin_series_two(0.7,100)
   print maclaurin_series3 

###################################################################
#"C:\python 
#0.990099009901
#0.917431192661
#0.671140939597
Tags: mathematics

1 comment

Fouad Teniou (author) 13 years, 7 months ago  # | flag

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