Online Help

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.

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

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

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

$1+x+\frac{1}{2}{x}^2+\frac{1}{3}{x}^3+\frac{1}{4}{x}^4+O\left(x^5\right)$

$r≔\mathrm{powint}\left(t\right)\:$

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

$x+\frac{1}{2}{x}^2+\frac{1}{6}{x}^3+\frac{1}{12}{x}^4+\frac{1}{20}{x}^5+\frac{1}{30}{x}^6+O\left(x^7\right)$