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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.

The Maclaurin's series for ln(1+x) could be used to approximate the natural logarithm ln(x).

Python, 65 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_ln is a function to compute ln(1+x) using maclaurin series
and the interval of convergence is -1 < x <= 1
ln(1+x) = x- x^2/2 +x^3/3 - x^4/4! + ...........
"""

from math import *

def error(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_ln(value,k):
    """
    Compute maclaurin's series approximation for ln(1+x).
    """
    
    global first_value    
    first_value = 0.0
    
    #attempt to Approximate ln(1+x) for a given value
    try:
        
        error(value)
        for item in xrange(1,k,2):
            next_value =(value**item)/float(item)
            first_value += next_value
            
        for item in xrange(2,k,2):
            next_value = -1*(value**item)/float(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__":
    
   macllaurin_ln1 =  maclaurin_ln(1,700000) # ln(2)
   print macllaurin_ln1
   macllaurin_ln2 =  maclaurin_ln(0.7,1000) 
   print macllaurin_ln2
   macllaurin_ln3 =  maclaurin_ln(0.3,1000) 
   print macllaurin_ln3

#####################################################################  
#"C:\python
#0.693147894846
#0.530628251062
#0.262364264467
#####################################################################

1 comment

Fouad Teniou (author) 11 years, 2 months ago  # | flag

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