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:

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.

$\mathrm{with}\left(\mathrm{powseries}\right)\:$

$\mathrm{powcreate}\left(f\left(n\right)=\frac{f\left(n-1\right)}{n}\,f\left(0\right)=1\right)\:$

$\mathrm{powcreate}\left(g\left(n\right)=\frac{g\left(n-1\right)}{2}\,g\left(0\right)=0\,g\left(1\right)=1\right)\:$

$\mathrm{powcreate}\left(h\left(n\right)=\frac{h\left(n-1\right)}{5}\,h\left(0\right)=1\right)\:$

$k≔\mathrm{evalpow}\left(f^3+g-\mathrm{powquo}\left(h\,f\right)\right)\:$

$\mathrm{tpsform}\left(k\,x\,5\right)$

$\frac{24}{5}x+\frac{233}{50}{x}^2+\frac{7273}{1500}{x}^3+\frac{52171}{15000}{x}^4+O\left(x^5\right)$

$b≔\mathrm{evalpow}\left(\mathrm{Diff}\left(\mathrm{powlog}\left(1+x\right)\right)\right)\:$

$c≔\mathrm{tpsform}\left(b\,x\,6\right)$

$c≔1-x+x^2-x^3+x^4-x^5+O\left(x^6\right)$

$e≔\mathrm{evalpow}\left(\mathrm{Tan}\left(1+x\right)\right)\:$

$f≔\mathrm{tpsform}\left(e\,x\,3\right)$

$f≔\frac{\sin \left(1\right)}{\cos \left(1\right)}+\frac{\cos \left(1\right)+\frac{{\sin \left(1\right)}^2}{\cos \left(1\right)}}{\cos \left(1\right)}x+\frac{\sin \left(1\right)\left(\cos \left(1\right)+\frac{{\sin \left(1\right)}^2}{\cos \left(1\right)}\right)}{{\cos \left(1\right)}^2}{x}^2+O\left(x^3\right)$

$g≔\mathrm{tpsform}\left(\mathrm{evalpow}\left(\sinh \left(x\right)\right)\,x\,8\right)$

$g≔x+\frac{1}{6}{x}^3+\frac{1}{120}{x}^5+\frac{1}{5040}{x}^7+O\left(x^8\right)$

$h≔\mathrm{evalpow}\left(\mathrm{powadd}\left(\mathrm{powexp}\left(x\right)\,\mathrm{powpoly}\left(1+x\,x\right)\,\mathrm{powlog}\left(1+x\right)\right)\right)\:$

$m≔\mathrm{tpsform}\left(h\,x\,8\right)$

$m≔2+3x+\frac{1}{2}{x}^3-\frac{5}{24}{x}^4+\frac{5}{24}{x}^5-\frac{119}{720}{x}^6+\frac{103}{720}{x}^7+O\left(x^8\right)$