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Maclaurin's_series_cosh (Python recipe) by Fouad Teniou
ActiveState Code (http://code.activestate.com/recipes/577286/)

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 series.

Hyperbolic functions are very common in the engineering field and they are related to trigonometric functions, thus, trigonometric functions could be expressed in terms of exponential(x) The hyperbolic cosine cosh(x) =(e^x + e^-x)/2.

Python, 47 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 : 06/07/10
#version :2.6

"""
maclaurin_cosh is a function to compute cosh(x) using maclaurin series
and the interval of convergence is -inf < x < +inf 
cosh(x) = 1+ x^2/2! + x^4/4! + x^6/6! ...........
"""

from math import *

def maclaurin_cosh(value, k):
    """
    Compute maclaurin's series approximation for cosh(x).
    """
    
    global first_value
    first_value = 0.0
    
    #attempt to Approximate cosh(x) for a given value
    try:
        for item in xrange(0,k,2):
            next_value =(value*pi/180)**item/factorial(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_cosh1 = maclaurin_cosh(70,100)
    print maclaurin_cosh1
    maclaurin_cosh2 = maclaurin_cosh(45,100)
    print maclaurin_cosh2
    maclaurin_cosh3 = maclaurin_cosh(30,100)
    print maclaurin_cosh3
######################################################################
#C:\python
#1.8438869882
#1.32460908925
#1.14023832108
Tags: mathematics