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.
There are several ways of finding Maclaurin’s series, and I used the multiplication and the division to develop my own maclaurin’s series for cos(2x) and cos²(x).
Cos(2x) = 2cos²(x) - 1 and cos²(x) = (cos(2x)+1)/2
However, integration and differentiation could also be used to find Maclaurin’s series.
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#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.
#Author : Fouad Teniou
#Date : 03/08/10
#version :2.6
"""
maclaurin_cos_pow2 is a function to compute cos(x) using maclaurin series
and the interval of convergence is -inf < x < +inf
cos²(x) = 1- x^2 + 2^3*x^4/4! - 2^5*x^6/6! ...........
"""
from math import *
def maclaurin_cos_pow2(value,k):
"""
Compute maclaurin's series approximation for cos^2(x).
"""
global first_value
first_value = 0.0
#attempt to Approximate cos^2(x) for a given value
try:
for item in xrange(4,k,4):
next_value = (2**(item-1))*(value*pi/180)**item/factorial(item)
first_value += next_value
for item in xrange(2,k,4):
next_value = -1*(2**(item-1))*((value*pi/180)**item/factorial(item))
first_value += next_value
return first_value +1
#Raise TypeError if input is not a number
except TypeError:
print 'Please enter an integer or a float value'
if __name__ == "__main__":
maclaurin_cos1 = maclaurin_cos_pow2(135,100)
print maclaurin_cos1
maclaurin_cos2 = maclaurin_cos_pow2(45,100)
print maclaurin_cos2
maclaurin_cos3 = maclaurin_cos_pow2(30,100)
print maclaurin_cos3
#############################################################
#FT python "C:
#0.5
#0.5
#0.75
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