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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 : 21/09/10
#version :2.6

"""
maclaurin_tanh-1 is a function to compute tanh-1(x) using maclaurin series
and the interval of convergence is -1 < x < +1 and -inf < y < +inf
tanh-1(y) = ln(1+y/1-y)/2 and y = 1+x/1-x
tanh-1(y) = x + x^3/3 + x^5/5 + x^7/7 ...........)
"""




def maclaurin_coth(value, k):
   
"""
    Compute maclaurin's series approximation for tanh-1(value).
    """

 
   
global first_value    
    first_value
= 0.0
   
   
#attempt to Approximate tanh-1(x) for a given value    
   
try:
        value_y
=float((1+value  )/(1-value))
        value_x
= (value_y -1)/float(value_y + 1)
       
for item in xrange(1,k,2):
            next_value
= value_x **item/item
            first_value
+= next_value

       
return 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_coth_1
= maclaurin_coth(0.3,100)
   
print maclaurin_coth_1
    maclaurin_coth_2
= maclaurin_coth(0.5,100)
   
print maclaurin_coth_2
    maclaurin_coth_3
= maclaurin_coth(0.7,100)
   
print maclaurin_coth_3  

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

#FT python "C:

#0.309519604203
#0.549306144334
#0.867300527694

 

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