powint - Maple Help

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powseries

 powint
 integration of a formal power series

 Calling Sequence powint(p) powseries[powint](p)

Parameters

 p - formal power series

Description

 • The function powint(p) returns the formal power series that is the formal anti-derivative of p with respect to the variable of the power series.
 • The command with(powseries,powint) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $\mathrm{powcreate}\left(t\left(n\right)=\frac{1}{n},t\left(0\right)=1\right):$
 > $\mathrm{tpsform}\left(t,x,5\right)$
 ${1}{+}{x}{+}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}\frac{{1}}{{3}}{}{{x}}^{{3}}{+}\frac{{1}}{{4}}{}{{x}}^{{4}}{+}{O}{}\left({{x}}^{{5}}\right)$ (1)
 > $r≔\mathrm{powint}\left(t\right):$
 > $\mathrm{tpsform}\left(r,x,7\right)$
 ${x}{+}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}\frac{{1}}{{12}}{}{{x}}^{{4}}{+}\frac{{1}}{{20}}{}{{x}}^{{5}}{+}\frac{{1}}{{30}}{}{{x}}^{{6}}{+}{O}{}\left({{x}}^{{7}}\right)$ (2)