quotient - Maple Help

powseries

 quotient
 quotient of two formal power series

 Calling Sequence quotient(a, b)

Parameters

 a, b - formal power series

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $\mathrm{powcreate}\left(t\left(n\right)=\frac{t\left(n-1\right)}{n},t\left(0\right)=1\right):$
 > $\mathrm{powcreate}\left(v\left(n\right)=\frac{v\left(n-1\right)}{5},v\left(0\right)=1\right):$
 > $s≔\mathrm{quotient}\left(t,v\right):$
 > $\mathrm{tpsform}\left(s,x,4\right)$
 ${1}{+}\frac{{4}}{{5}}{}{x}{+}\frac{{3}}{{10}}{}{{x}}^{{2}}{+}\frac{{1}}{{15}}{}{{x}}^{{3}}{+}{O}{}\left({{x}}^{{4}}\right)$ (1)