Maclaurin series

Meaning

Noun

• Any Taylor series that is centred at 0 (i.e., for which the origin is the reference point used to derive the series from its associated function); for a given infinitely differentiable complex function $\backslash textstyle\; f$, the power series $\backslash textstyle\; f(0)+\backslash frac\; \{f\text{'}(0)\}\{1!\}x+\; \backslash frac\{f(0)\}\{2!\}x^2+\; \backslash frac\{f\text{'}(0)\}\{3!\}x^3+\; \backslash cdots\; =\; \backslash sum\_\{n=0\}^\{\backslash infty\}\; \backslash frac\{f^\{(n)\}(0)\}\{n!\}\; \backslash ,\; x^\{n\}$.

Related

Broader meaning words

• power series, Taylor series

Origin

• Named after Scottish mathematician Colin Maclaurin (1698-1746), who made extensive use of the series.