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.
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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 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
|
Tags: mathematics
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