VectorCalculus - Maple Programming Help

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VectorCalculus

 series
 map the top-level series function over a Vector

 Calling Sequence series(f, v)

Parameters

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

Description

 • The series(f, v) command 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

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