Taylor series

Meaning

Noun

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

Related

Narrower meaning words

• Maclaurin series

Origin

• Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.