The taylor command computes the order n Taylor series expansion of expression, with respect to the variable x, about the point a.

The taylor command is thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe.

$\mathrm{taylor}\left(\exp \left(x\right)\,x=0\,4\right)$

$1+x+\frac{1}{2}{x}^2+\frac{1}{6}{x}^3+O\left(x^4\right)$

$\mathrm{taylor}\left(\frac{1}{x}\,x=1\,3\right)$

$1-\left(x-1\right)+{\left(x-1\right)}^2+O\left({\left(x-1\right)}^3\right)$

$\mathrm{taylor}\left(\sin \left(x\right)\,x=\mathrm{\pi }\right)$

$-\left(x-\mathrm{\pi }\right)+\frac{1}{6}{\left(x-\mathrm{\pi }\right)}^3-\frac{1}{120}{\left(x-\mathrm{\pi }\right)}^5+O\left({\left(x-\mathrm{\pi }\right)}^7\right)$

$\mathrm{taylor}\left(\mathrm{sqrt}\left(1+x\right)\,x\,8\right)$

$1+\frac{1}{2}x-\frac{1}{8}{x}^2+\frac{1}{16}{x}^3-\frac{5}{128}{x}^4+\frac{7}{256}{x}^5-\frac{21}{1024}{x}^6+\frac{33}{2048}{x}^7+O\left(x^8\right)$

$\mathrm{taylor}\left(\mathrm{sqrt}\left(1+x\right)\,x=0\,8\right)$

$1+\frac{1}{2}x-\frac{1}{8}{x}^2+\frac{1}{16}{x}^3-\frac{5}{128}{x}^4+\frac{7}{256}{x}^5-\frac{21}{1024}{x}^6+\frac{33}{2048}{x}^7+O\left(x^8\right)$

For detailed information including:

Optional parameters

Converting a Taylor series to a polynomial

The general series command

see the taylor/details help page.