#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 : 10/07/10
#version :2.6
"""
maclaurin_ln is a function to compute ln(x) using maclaurin series
and the interval of convergence is -1 < x < +1
ln(y) = ln(1+x/1-x)= 2(x + x^3/3 + x^5/5 + x^7/7 ...........)
"""
def maclaurin_ln(value, k):
"""
Compute maclaurin's series approximation for ln(value).
"""
global first_value
first_value = 0.0
#attempt to Approximate sinh(x) for a given value
try:
value_x = (value - 1)/float(value + 1)
for item in xrange(1,k,2):
next_value = value_x **item/item
first_value += next_value
return 2*(first_value)
#Raise TypeError if input is not a number
except TypeError:
print 'Please enter an integer or a float value'
if __name__ == "__main__":
maclaurin_ln_1 = maclaurin_ln(2,100)
print maclaurin_ln_1
maclaurin_ln_2 = maclaurin_ln(5,100)
print maclaurin_ln_2
maclaurin_ln_3 = maclaurin_ln(777,10000)
print maclaurin_ln_3
print
for arg in xrange(7,28,10):
print "ln(%s) = %s " %\
(arg, maclaurin_ln(arg,10000))
###########################################################################
"C: python \Maclaurin_ln
0.69314718056
1.60943791243
6.65544035037
ln(7) = 1.94591014906
ln(17) = 2.83321334406
ln(27) = 3.295836866
Diff to Previous Revision
--- revision 1 2010-07-10 12:48:44
+++ revision 2 2010-07-15 10:46:28
@@ -10,7 +10,6 @@
ln(y) = ln(1+x/1-x)= 2(x + x^3/3 + x^5/5 + x^7/7 ...........)
"""
-from math import *
def maclaurin_ln(value, k):
"""
@@ -55,8 +54,3 @@
ln(7) = 1.94591014906
ln(17) = 2.83321334406
ln(27) = 3.295836866
-
-###################################################################
-the maclaurin's series approximation for ln(1+x) is used to approximate ln(x) by detucting the maclaurin's series for ln(1-x).
-ln(1+x) - ln(1-x) = ln(1+x/1-x)and by letting y = (1+x/1-x), y could take any positive value.
-y = 1+x/1-x, therefore x = y-1/y+1 -1<x<1
