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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.

The Maclaurin's series to approximate ( 1+x)^m is known as a binomial series.

However, if m is a an integer and m >= 0 the function f(x ) = (1+x)^m is a polynomial function of degree m and it will converge for all the values of x on the interval ]-inf, +inf [, otherwise it will converge to (1+x)^m only for the values of x on the interval ]-1,1[, thus, the convergence of x will depend on the value of m

Python, 163 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 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163``` ```#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_binomial is a function to compute(1+x)^m using maclaurin binomial series and the interval of convergence is -1 < x < 1 (1+x)^m = 1 + mx + m(m-1)x^2/2! + m(m-1)(m-2)x^3/3!........... note: if m is a nonegative integer the binomial is a polynomial of degree m and it is valid on -inf < x < +inf,thus, the error function will not be valid. """ from math import * def error(number): """ Raises interval of convergence error.""" if number >= 1 or number <= -1 : raise TypeError,\ "\n= 1 or number <= -1 : # raise TypeError("\n

Fouad Teniou (author) 13 years, 7 months ago

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

Fouad Teniou (author) 12 years, 8 months ago

A switch to C# and a new link