powcos - Maple Help

powseries

 powcos
 compute the formal power series equal to the cosine of an expression

 Calling Sequence powcos(p)

Parameters

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

Description

 • The function powcos(p) returns the formal power series that is equivalent to cos(p).
 • The powseries function evalpow accepts the form in either powcos, Cos, or cos.
 • The command with(powseries,powcos) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $a≔\mathrm{powcos}\left(x+1\right):$
 > $b≔\mathrm{tpsform}\left(a,x,5\right)$
 ${b}{≔}{\mathrm{cos}}{}\left({1}\right){-}{\mathrm{sin}}{}\left({1}\right){}{x}{-}\frac{{1}}{{2}}{}{\mathrm{cos}}{}\left({1}\right){}{{x}}^{{2}}{+}\frac{{1}}{{6}}{}{\mathrm{sin}}{}\left({1}\right){}{{x}}^{{3}}{+}\frac{{1}}{{24}}{}{\mathrm{cos}}{}\left({1}\right){}{{x}}^{{4}}{+}{O}{}\left({{x}}^{{5}}\right)$ (1)
 > $c≔\mathrm{evalpow}\left(\mathrm{Cos}\left(\mathrm{log}\left(1+x\right)\right)\right):$
 > $d≔\mathrm{tpsform}\left(c,x,5\right)$
 ${d}{≔}{1}{-}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}\frac{{1}}{{2}}{}{{x}}^{{3}}{-}\frac{{5}}{{12}}{}{{x}}^{{4}}{+}{O}{}\left({{x}}^{{5}}\right)$ (2)
 > $e≔\mathrm{powdiff}\left(\mathrm{powcos}\left(x\right)\right):$
 > $f≔\mathrm{tpsform}\left(e,x,6\right)$
 ${f}{≔}{-}{x}{+}\frac{{1}}{{6}}{}{{x}}^{{3}}{-}\frac{{1}}{{120}}{}{{x}}^{{5}}{+}{O}{}\left({{x}}^{{6}}\right)$ (3)
 > $g≔\mathrm{evalpow}\left(\mathrm{tan}\left({x}^{2}\right)\right):$
 > $h≔\mathrm{tpsform}\left(g,x,10\right)$
 ${h}{≔}{{x}}^{{2}}{+}\frac{{1}}{{3}}{}{{x}}^{{6}}{+}{O}{}\left({{x}}^{{10}}\right)$ (4)