compose - Maple Help

powseries

 compose
 composition of formal power series

 Calling Sequence compose(a, b)

Parameters

 a, b - formal power series

Description

 • The function compose(a, b) computes and returns the formal power series $a\left(b\right)$, the composition of a and b. This power series is: $a\left(0\right)+a\left(1\right)b+a\left(2\right){b}^{2}+a\left(3\right){b}^{3}+...$.
 • Note that $b\left(0\right)$ must be 0 to ensure that the composition is well defined.  Otherwise, compose returns an error message.
 • The command with(powseries,compose) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $\mathrm{powcreate}\left(t\left(n\right)=\frac{t\left(n-1\right)}{n},t\left(0\right)=1\right):$
 > $\mathrm{powcreate}\left(v\left(n\right)=\frac{v\left(n-1\right)}{2},v\left(0\right)=0,v\left(1\right)=1\right):$
 > $s≔\mathrm{compose}\left(t,v\right):$
 > $\mathrm{tpsform}\left(s,x\right)$
 ${1}{+}{x}{+}{{x}}^{{2}}{+}\frac{{11}}{{12}}{}{{x}}^{{3}}{+}\frac{{19}}{{24}}{}{{x}}^{{4}}{+}\frac{{157}}{{240}}{}{{x}}^{{5}}{+}{O}{}\left({{x}}^{{6}}\right)$ (1)