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Maclaurin's_series_tanh-1(x) (Python recipe) by Fouad Teniou
ActiveState Code (http://code.activestate.com/recipes/577399/)

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's series.

Natural logarithms are used to compute inverse hyperbolic functions.

Python, 53 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 : 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
Tags: mathematics

1 comment

Fouad Teniou (author) 13 years, 7 months ago  # | flag

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