#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_sinh-1 is a function to compute sinh-1(x) using maclaurin series
and the interval of convergence is -1 < x < +1 and -inf < y < +inf
sinh-1(y) = ln(y + sqrt(y**2 +1)= and y = ln(1+x/1-x) =
sinh-1(y) = 2(x + x^3/3 + x^5/5 + x^7/7 ...........)
"""
from math import *
def maclaurin_sinh_inverse(value, k):
"""
Compute maclaurin's series approximation for sinh-1(value).
"""
global first_value
first_value = 0.0
#attempt to Approximate sinh-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_sinh_inverse1 = maclaurin_sinh_inverse(1,100)
print maclaurin_sinh_inverse1
maclaurin_sinh_inverse2 = maclaurin_sinh_inverse(2,100)
print maclaurin_sinh_inverse2
maclaurin_sinh_inverse3 = maclaurin_sinh_inverse(3,100)
print maclaurin_sinh_inverse3
######################################################################FT python "C:
#0.88137358702
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