Series Approximations

Calculus, Numerical-Methods

Maclaurin Series

The Maclaurin Series of a function is an approximation for a function at x=0. (many common functions are exactly equal their Maclaurin expansion and are called analytical functions) The Maclaurin series for a function that is infinitely Differentiable at is given by:

This expansion only if exists and for values of for which the series Converges.

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Taylor Series

A Taylor series is simply just a that is centred at some value rather than and is given by the formula:

where is the value for which the Taylor Series is centred. This expansion only if exists and for values of for which the series Converges.