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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 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 sine sinh(x) = (e^x - e^-x)/2.

Python, 47 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 51``` ```#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_sinh is a function to compute sinh(x) using maclaurin series and the interval of convergence is -inf < x < +inf sinh(x) = x + x^3/3! + x^5/5! + x^7/7! ........... """ from math import * def maclaurin_sinh(value, k): """ Compute maclaurin's series approximation for sinh(x) """ global first_value first_value = 0.0 #attempt to Approximate sinh(x) for a given value try: for item in xrange(1,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_sinh1 = maclaurin_sinh(70,100) print maclaurin_sinh1 maclaurin_sinh2 = maclaurin_sinh(45,100) print maclaurin_sinh2 maclaurin_sinh3 = maclaurin_sinh(30,100) print maclaurin_sinh3 ######################################################################"C:\python #1.54916726832 #0.868670961486 #0.547853473888 ##################################################################### ```

#### 1 comment Fouad Teniou (author) 13 years ago Created by Fouad Teniou on Wed, 7 Jul 2010 (MIT)