powexp - Maple Help

powseries

 powexp
 compute the formal power series of the exponentiation of an expression

 Calling Sequence powexp(p)

Parameters

 p - formal power series, polynomial, or any function that is acceptable by the power series package functions

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $s≔\mathrm{powexp}\left(x\right):$
 > $\mathrm{tpsform}\left(s,x,7\right)$
 ${1}{+}{x}{+}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}\frac{{1}}{{24}}{}{{x}}^{{4}}{+}\frac{{1}}{{120}}{}{{x}}^{{5}}{+}\frac{{1}}{{720}}{}{{x}}^{{6}}{+}{O}{}\left({{x}}^{{7}}\right)$ (1)
 > $t≔\mathrm{powexp}\left(\mathrm{exp}\left(x\right)\right):$
 > $\mathrm{tpsform}\left(t,x,4\right)$
 ${ⅇ}{+}{ⅇ}{}{x}{+}{ⅇ}{}{{x}}^{{2}}{+}\frac{{5}}{{6}}{}{ⅇ}{}{{x}}^{{3}}{+}{O}{}\left({{x}}^{{4}}\right)$ (2)
 > $u≔\mathrm{powexp}\left(\mathrm{powdiff}\left(\mathrm{powlog}\left(1+x\right)\right)\right):$
 > $\mathrm{tpsform}\left(u,x,5\right)$
 ${ⅇ}{-}{ⅇ}{}{x}{+}\frac{{3}}{{2}}{}{ⅇ}{}{{x}}^{{2}}{-}\frac{{13}}{{6}}{}{ⅇ}{}{{x}}^{{3}}{+}\frac{{73}}{{24}}{}{ⅇ}{}{{x}}^{{4}}{+}{O}{}\left({{x}}^{{5}}\right)$ (3)