Taylor Series
Function as an infinite sum of terms.
A Taylor serie is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point. The generic expression:
f(x) = f(a) + f'(a) (x - a) / 1! + f''(a) (x - a)2 / 2! + ..... (1)
Examples
ex = 1 + x / 1! + x2 / 2! + x3/ 3! + ... (2)
ax = 1 + x ln a / 1! + (x ln a)2 / 2! + (x ln a)3 / 3! + .. (3)
ln x = 2( (x - 1) / (x + 1) + 1/3 ((x - 1) / (x + 1))3 + 1/5 ((x - 1) / (x + 1))5 + .. ) (4)
ln (1 + x) = x - x2 / 2 + x3/ 3 - x4 / 4 + x5/ 5 + ... (5)
sin x = x - x3 / 3! + x5/ 5! - x7 / 7! + ... (6)
cos x = 1 - x2 / 2! + x4/ 4! - x6 / 6! + ... (7)
tan x = x + 1/3 x3 + 2 /15 x5 + 17 / 315 x7 + ... (8)
Related Topics
-
Mathematics
Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.
Related Documents
-
Differential Calculus
Derivatives and differentiation expressions. -
Fractions
Law of fractions -
Hyperbolic Functions
Exponential functions related to the hyperbola. -
Law of Sines
Calculate the angles in a generic triangle. -
Polar vs. Cartesian Coordinates
Convert between Cartesian and Polar coordinates. -
Scientific and Engineering Terms - ANSI Abbreviations
Abbreviations for Use on Drawings and in Text - ANSI Y1.1. -
Trigonometric Functions
Sine, cosine and tangent - the natural trigonometric functions. -
Vector Addition
Online vector calculator - add vectors with different magnitude and direction - like forces, velocities and more.
