Series expansion

In mathematics, a series expansion is an expansion of a function into a series, or infinite sum.[1] It is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication and division).[2]

An animation showing the cosine function being approximated by successive truncations of its Maclaurin series.

The resulting so-called series often can be limited to a finite number of terms, thus yielding an approximation of the function. The fewer terms of the sequence are used, the simpler this approximation will be. Often, the resulting inaccuracy (i.e., the partial sum of the omitted terms) can be described by an equation involving Big O notation (see also asymptotic expansion). The series expansion on an open interval will also be an approximation for non-analytic functions.[3][verification needed]


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