Maclaurin's_series_sinh-1(x)

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.

#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
#1.44363547518
#1.81844645923


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>>17
                                           Heroes' key

1. A shame the blast of wind broke the silent bird´s wing.

2. Swing the cradle though I heard a cry and tears´ drops sound loud.

3. Sample of blood and a feather fell by the river it seems sad.

4. Scared no where to hide though the bright light site swelled.

5. Screams I heard in my dream an innocent shepherd a sheep lay asleep but never woke to the click.

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7. Sad I felt and searched my books though only peoples´ pictures deprived of looks yet no title but ghosts.

8. Short story yet mute not a dispute though only children playing but never
finished their game.

9. Slam the door without the frame a shame no one to blame yet a stain of a stark pain.

10. Sway the satin veil and spill the truth though a butterfly wing and ginger root lay inside a pot.

11. Spot the red mote and wipe with a cloth though dirt in black made it dark I turned on the light.

12. Sight of a rot a stone a mirror and a fork though the sun reflected the silver jewellery´s slot.
13. Shot the swine and free the land though a little to spend yet the garment dye lacks a blend.

14. Sands´ grains and a handful drops of rain made the jar plain though the sheep wool wove the sliver thread chain.

15. Stain on the mirror reflected the shadow of the hatred sun yet dark shrouded at dawn dearth the moon.

16. Soon I woke to a thunder though my lightning dreams faded in the lake searching for the heroes´ key.

17. Sky-high I gazed the missing clue though a nature blow yet the fingers´ prints on paper and wet inks in red spread the curse on the sailer.

18. Spoiler lacking a track I thought of the eight-legged spider wack though it stack hanging in the drapes and fell inside a cruse to a smack.

19. Slack the net´s strings swung through the sea-waves for nights though fishing lacking a sight needed a match and a candle light. 

20. Shut the gates though it´s too late yet Japanese´ faith never die a shark brake. 

21. Storm of flake.

Fouad Teniou Copyright 13/11/08
 


Dedicated to all heroes who died in Hiroshima and Nagasaki in 1945 and all
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