converting series - Maple Help

convert/polynom

convert a series to polynomial form

 Calling Sequence convert( series, polynom )

Parameters

 series - series; preferably of type taylor

Description

 • Convert to polynom converts a Taylor series to a polynomial. If series is not a Taylor series then the conversion to sum-of-products form takes place but the result is not of type polynom.

Examples

 > $s≔\mathrm{series}\left(\mathrm{sin}\left(x\right),x,5\right)$
 ${s}{≔}{x}{-}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}{O}{}\left({{x}}^{{5}}\right)$ (1)
 > $\mathrm{type}\left(s,\mathrm{polynom}\right)$
 ${\mathrm{false}}$ (2)
 > $p≔\mathrm{convert}\left(s,\mathrm{polynom}\right)$
 ${p}{≔}{x}{-}\frac{{1}}{{6}}{}{{x}}^{{3}}$ (3)
 > $\mathrm{type}\left(p,\mathrm{polynom}\left(\mathrm{anything},x\right)\right)$
 ${\mathrm{true}}$ (4)
 > $t≔\mathrm{series}\left(\frac{\mathrm{exp}\left(x\right)}{x},x,3\right)$
 ${t}{≔}{{x}}^{{-1}}{+}{1}{+}\frac{{1}}{{2}}{}{x}{+}{O}{}\left({{x}}^{{2}}\right)$ (5)
 > $q≔\mathrm{convert}\left(t,\mathrm{polynom}\right)$
 ${q}{≔}\frac{{1}}{{x}}{+}{1}{+}\frac{{x}}{{2}}$ (6)
 > $\mathrm{type}\left(q,\mathrm{polynom}\left(\mathrm{anything},x\right)\right)$
 ${\mathrm{false}}$ (7)
 > $\mathrm{type}\left(q,\mathrm{+}\right)$
 ${\mathrm{true}}$ (8)