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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, 50 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50``` ```#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 ```

#### 2 comments

Fouad Teniou (author) 13 years, 5 months ago

My profile,poems, photos,and design's links

https://acrobat.com/#d=aEjxtq78QkGKUxa*UprkZQ

Fouad Teniou (author) 12 years, 7 months ago

A switch to C# and a new link

http://archive.msdn.microsoft.com/fouadteniou

 Created by Fouad Teniou on Tue, 21 Sep 2010 (MIT)