#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
