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.
The natural exponential function e^x has a constant base e and a variable x and Maclaurin's series to approximate the natural exponential converge on the interval ]-inf , + inf [.
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Copy to clipboard1 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 | #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_expenantial is a function to compute e^x using maclaurin series
and the interval of convergence is -inf < x < + inf
e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! ...........
"""
from math import *
def maclaurin_expenantial(value, k):
"""
Compute maclaurin's series approximation for e^x
"""
first_value = 0.0
#attempt to Approximate e^x for a given value
try:
for item in xrange(k):
next_value = float(value**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_exp1 = maclaurin_expenantial(1,100)
print maclaurin_exp1
maclaurin_exp2 = maclaurin_expenantial(3,100)
print maclaurin_exp2
maclaurin_exp3 = maclaurin_expenantial(7,100)
print maclaurin_exp3
#####################################################################
#"C:python
#urine series\
#2.71828182846
#20.0855369232
#1096.63315843
#####################################################################
|
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