#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
#####################################################################
