 powcreate - Maple Help

powseries

 powcreate
 create formal power series Calling Sequence powcreate(eqns) Parameters

 eqns - expression sequence of equations Description

 • The function powcreate creates a formal power series whose coefficients are specified by eqns.
 • The expression sequence of equations passed to powcreate should consist of one equation, possibly recursive, that specifies the nth coefficient, followed by zero or more equations that specify initial conditions.
 • More specifically, powcreate(t(n)=expr, t(0)=a0, ..., t(m)=am) creates a formal power series, t, whose nth coefficient is expr, and whose initial terms are $t\left(0\right)=\mathrm{a0}$, ..., $t\left(m\right)=\mathrm{am}$.
 • Any initial conditions among eqns override the general expression.  Thus, it is possible to include particular values of coefficients in eqns.
 • The command with(powseries,powcreate) allows the use of the abbreviated form of this command. Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $\mathrm{powcreate}\left(t\left(n\right)=\frac{1}{n!},t\left(0\right)=1\right):$
 > $\mathrm{tpsform}\left(t,x,7\right)$
 ${1}{+}{x}{+}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}\frac{{1}}{{24}}{}{{x}}^{{4}}{+}\frac{{1}}{{120}}{}{{x}}^{{5}}{+}\frac{{1}}{{720}}{}{{x}}^{{6}}{+}{O}{}\left({{x}}^{{7}}\right)$ (1)
 > $\mathrm{powcreate}\left(v\left(n\right)=\frac{v\left(n-1\right)+v\left(n-2\right)}{4},v\left(0\right)=4,v\left(1\right)=2\right):$
 > $\mathrm{tpsform}\left(v,x\right)$
 ${4}{+}{2}{}{x}{+}\frac{{3}}{{2}}{}{{x}}^{{2}}{+}\frac{{7}}{{8}}{}{{x}}^{{3}}{+}\frac{{19}}{{32}}{}{{x}}^{{4}}{+}\frac{{47}}{{128}}{}{{x}}^{{5}}{+}{O}{}\left({{x}}^{{6}}\right)$ (2)