series - Maple Help

Student[VectorCalculus]

 series
 compute the series expansion of each component of a Vector

 Calling Sequence series(f, v)

Parameters

 f - Vector or algebraic expression v - expression sequence of arguments to pass to the top-level series function

Description

 • The series(f, v) calling sequence maps the top-level series function over the components of the Vector f.  If f is not a Vector, the arguments are passed to the top-level series function.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right):$
 > $\mathrm{series}\left(⟨\mathrm{sin}\left(t\right),\mathrm{exp}\left(t\right)⟩,t=0\right)$
 $\left({t}{-}\frac{{1}}{{6}}{}{{t}}^{{3}}{+}\frac{{1}}{{120}}{}{{t}}^{{5}}{+}{O}{}\left({{t}}^{{7}}\right)\right){{e}}_{{x}}{+}\left({1}{+}{t}{+}\frac{{1}}{{2}}{}{{t}}^{{2}}{+}\frac{{1}}{{6}}{}{{t}}^{{3}}{+}\frac{{1}}{{24}}{}{{t}}^{{4}}{+}\frac{{1}}{{120}}{}{{t}}^{{5}}{+}{O}{}\left({{t}}^{{6}}\right)\right){{e}}_{{y}}$ (1)
 > $\mathrm{series}\left(⟨\frac{\mathrm{sin}\left(t\right)}{t},\frac{1-\mathrm{cos}\left(t\right)}{t}⟩,t=0\right)$
 $\left({1}{-}\frac{{1}}{{6}}{}{{t}}^{{2}}{+}\frac{{1}}{{120}}{}{{t}}^{{4}}{+}{O}{}\left({{t}}^{{6}}\right)\right){{e}}_{{x}}{+}\left(\frac{{1}}{{2}}{}{t}{-}\frac{{1}}{{24}}{}{{t}}^{{3}}{+}{O}{}\left({{t}}^{{5}}\right)\right){{e}}_{{y}}$ (2)
 > $\mathrm{series}\left(\mathrm{log}\left(1+z\right),z\right)$
 ${z}{-}\frac{{1}}{{2}}{}{{z}}^{{2}}{+}\frac{{1}}{{3}}{}{{z}}^{{3}}{-}\frac{{1}}{{4}}{}{{z}}^{{4}}{+}\frac{{1}}{{5}}{}{{z}}^{{5}}{+}{O}{}\left({{z}}^{{6}}\right)$ (3)