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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.
#Date : 21/09/10
#version :2.6

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

from math import *

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

global first_value
first_value = 0.0

#attempt to Approximate cosh-1(x) for a given value
try:
value_y = value + sqrt(value**2-1)
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 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_cosh_inverse1 = maclaurin_cosh_inverse(3,100)
print maclaurin_cosh_inverse1
maclaurin_cosh_inverse2 = maclaurin_cosh_inverse(5,100)
print maclaurin_cosh_inverse2
maclaurin_cosh_inverse3 = maclaurin_cosh_inverse(7,100)
print maclaurin_cosh_inverse3

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

#FT python "C:
#1.76274717404
#2.29243166949
#2.63391575704