Taylor series

English

Alternative forms

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Etymology

Named after English mathematician Template:W, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician Template:W.

Noun

1. Template:Lb A power series representation of given infinitely differentiable function $f$ whose terms are calculated from the function's arbitrary order derivatives at given reference point $a$; the series $f(a)+\frac{f^{\prime }(a)}{1!}(x-a)+\frac{f^{″}(a)}{2!}(x-a{)}^2+\frac{f^{‴}(a)}{3!}(x-a{)}^3+\cdots ={\sum }_{n=0}^{\mathrm{\infty }}\frac{f^{(n)}(a)}{n!}(x-a{)}^n$.
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Hyponyms

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