The function quotient(a, b) returns the formal power series equal to a/b .

This function yields the same result as $\mathrm{multiply}\left(a\,\mathrm{inverse}\left(b\right)\right)$, but is faster.

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

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

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

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

$s≔\mathrm{quotient}\left(t\,v\right)\:$

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

$1+\frac{4}{5}x+\frac{3}{10}{x}^2+\frac{1}{15}{x}^3+O\left(x^4\right)$