powseries - Maple Programming Help

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powseries

 powsin
 compute the formal power series equal to the sine of an expression

 Calling Sequence powsin(p)

Parameters

 p - formal power series, polynomial, or any function that is acceptable for power series package

Description

 • The function powsin(p) returns the formal power series that is equivalent to $\mathrm{sin}\left(p\right)$.
 • The powseries function evalpow accepts the form as any of powsin, Sin, or sin.
 • The command with(powseries,powsin) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $a≔\mathrm{powsin}\left({x}^{2}\right):$
 > $b≔\mathrm{tpsform}\left(a,x,10\right)$
 ${b}{:=}{{x}}^{{2}}{-}\frac{{1}}{{6}}{}{{x}}^{{6}}{+}{\mathrm{O}}\left({{x}}^{{10}}\right)$ (1)
 > $c≔\mathrm{evalpow}\left(\mathrm{sin}\left({ⅇ}^{x}\right)\right):$
 > $d≔\mathrm{tpsform}\left(c,x,5\right)$
 ${d}{:=}{\mathrm{sin}}{}\left({1}\right){+}{\mathrm{cos}}{}\left({1}\right){}{x}{+}\left({-}\frac{{1}}{{2}}{}{\mathrm{sin}}{}\left({1}\right){+}\frac{{1}}{{2}}{}{\mathrm{cos}}{}\left({1}\right)\right){}{{x}}^{{2}}{-}\frac{{1}}{{2}}{}{\mathrm{sin}}{}\left({1}\right){}{{x}}^{{3}}{+}\left({-}\frac{{5}}{{24}}{}{\mathrm{cos}}{}\left({1}\right){-}\frac{{1}}{{4}}{}{\mathrm{sin}}{}\left({1}\right)\right){}{{x}}^{{4}}{+}{\mathrm{O}}\left({{x}}^{{5}}\right)$ (2)
 > $e≔\mathrm{powdiff}\left(\mathrm{powsin}\left(x\right)\right):$
 > $f≔\mathrm{tpsform}\left(e,x,6\right)$
 ${f}{:=}{1}{-}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}\frac{{1}}{{24}}{}{{x}}^{{4}}{+}{\mathrm{O}}\left({{x}}^{{6}}\right)$ (3)