evalpow - Maple Help

powseries

 evalpow
 general evaluator for expressions, which can be formal power series, polynomials, or functions

 Calling Sequence evalpow(expr)

Parameters

 expr - any arithmetic expression involving formal power series, polynomials, or functions that is acceptable for power series package

Description

 • The function evalpow(expr) evaluates the arithmetic expression expr and then returns an unnamed power series.
 • The following operators can be used: $+$, $-$, , $/$, and $^$.
 • Also, functions may be composed with each other. For example, $f\left(g\right)$ can be used.
 • The other functions that can be used in evalpow are:

 powexp powinv powlog powneg powrev (reversion) powdiff (first derivative) powint (first integral) powquo (quotient) powsub (subtract) powsin powcos powtan powsec powcsc powcot powsinh powcosh powtanh powsech powcsch powcoth powsqrt(square root) powadd multiply

 • Note that the evalpow also accepts the standard forms, or the inner MAPLE forms for some of the above functions. For example, exp, or Exp for powexp, Diff for powdiff, but NOT diff.
 • The command with(powseries,evalpow) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $\mathrm{powcreate}\left(f\left(n\right)=\frac{f\left(n-1\right)}{n},f\left(0\right)=1\right):$
 > $\mathrm{powcreate}\left(g\left(n\right)=\frac{g\left(n-1\right)}{2},g\left(0\right)=0,g\left(1\right)=1\right):$
 > $\mathrm{powcreate}\left(h\left(n\right)=\frac{h\left(n-1\right)}{5},h\left(0\right)=1\right):$
 > $k≔\mathrm{evalpow}\left({f}^{3}+g-\mathrm{powquo}\left(h,f\right)\right):$
 > $\mathrm{tpsform}\left(k,x,5\right)$
 $\frac{{24}}{{5}}{}{x}{+}\frac{{233}}{{50}}{}{{x}}^{{2}}{+}\frac{{7273}}{{1500}}{}{{x}}^{{3}}{+}\frac{{52171}}{{15000}}{}{{x}}^{{4}}{+}{O}{}\left({{x}}^{{5}}\right)$ (1)
 > $b≔\mathrm{evalpow}\left(\mathrm{Diff}\left(\mathrm{powlog}\left(1+x\right)\right)\right):$
 > $c≔\mathrm{tpsform}\left(b,x,6\right)$
 ${c}{≔}{1}{-}{x}{+}{{x}}^{{2}}{-}{{x}}^{{3}}{+}{{x}}^{{4}}{-}{{x}}^{{5}}{+}{O}{}\left({{x}}^{{6}}\right)$ (2)
 > $e≔\mathrm{evalpow}\left(\mathrm{Tan}\left(1+x\right)\right):$
 > $f≔\mathrm{tpsform}\left(e,x,3\right)$
 ${f}{≔}\frac{{\mathrm{sin}}{}\left({1}\right)}{{\mathrm{cos}}{}\left({1}\right)}{+}\frac{{\mathrm{cos}}{}\left({1}\right){+}\frac{{{\mathrm{sin}}{}\left({1}\right)}^{{2}}}{{\mathrm{cos}}{}\left({1}\right)}}{{\mathrm{cos}}{}\left({1}\right)}{}{x}{+}\frac{{\mathrm{sin}}{}\left({1}\right){}\left({\mathrm{cos}}{}\left({1}\right){+}\frac{{{\mathrm{sin}}{}\left({1}\right)}^{{2}}}{{\mathrm{cos}}{}\left({1}\right)}\right)}{{{\mathrm{cos}}{}\left({1}\right)}^{{2}}}{}{{x}}^{{2}}{+}{O}{}\left({{x}}^{{3}}\right)$ (3)
 > $g≔\mathrm{tpsform}\left(\mathrm{evalpow}\left(\mathrm{sinh}\left(x\right)\right),x,8\right)$
 ${g}{≔}{x}{+}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}\frac{{1}}{{120}}{}{{x}}^{{5}}{+}\frac{{1}}{{5040}}{}{{x}}^{{7}}{+}{O}{}\left({{x}}^{{8}}\right)$ (4)
 > $h≔\mathrm{evalpow}\left(\mathrm{powadd}\left(\mathrm{powexp}\left(x\right),\mathrm{powpoly}\left(1+x,x\right),\mathrm{powlog}\left(1+x\right)\right)\right):$
 > $m≔\mathrm{tpsform}\left(h,x,8\right)$
 ${m}{≔}{2}{+}{3}{}{x}{+}\frac{{1}}{{2}}{}{{x}}^{{3}}{-}\frac{{5}}{{24}}{}{{x}}^{{4}}{+}\frac{{5}}{{24}}{}{{x}}^{{5}}{-}\frac{{119}}{{720}}{}{{x}}^{{6}}{+}\frac{{103}}{{720}}{}{{x}}^{{7}}{+}{O}{}\left({{x}}^{{8}}\right)$ (5)