The function powexp(p) returns the formal power series that is equivalent to exp(p).

The command with(powseries,powexp) allows the use of the abbreviated form of this command.

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

$s≔\mathrm{powexp}\left(x\right)\:$

$\mathrm{tpsform}\left(s\,x\,7\right)$

$1+x+\frac{1}{2}{x}^2+\frac{1}{6}{x}^3+\frac{1}{24}{x}^4+\frac{1}{120}{x}^5+\frac{1}{720}{x}^6+O\left(x^7\right)$

$t≔\mathrm{powexp}\left(\exp \left(x\right)\right)\:$

$\mathrm{tpsform}\left(t\,x\,4\right)$

$\ⅇ+\ⅇx+\ⅇx^2+\frac{5}{6}\ⅇx^3+O\left(x^4\right)$

$u≔\mathrm{powexp}\left(\mathrm{powdiff}\left(\mathrm{powlog}\left(1+x\right)\right)\right)\:$

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

$\ⅇ-\ⅇx+\frac{3}{2}\ⅇx^2-\frac{13}{6}\ⅇx^3+\frac{73}{24}\ⅇx^4+O\left(x^5\right)$