powseries - Maple Programming Help

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powseries

 powdiff
 differentiation of a formal power series

 Calling Sequence powdiff(p)

Parameters

 p - formal power series

Description

 • The function powdiff(p) returns the formal power series that is the derivative of p with respect to the variable of p.
 • The command with(powseries,powdiff) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $t≔\mathrm{powpoly}\left(x+1,x\right):$
 > $s≔\mathrm{powlog}\left(t\right):$
 > $\mathrm{tpsform}\left(s,x,6\right)$
 ${x}{-}\frac{{1}}{{2}}{}{{x}}^{{2}}{+}\frac{{1}}{{3}}{}{{x}}^{{3}}{-}\frac{{1}}{{4}}{}{{x}}^{{4}}{+}\frac{{1}}{{5}}{}{{x}}^{{5}}{+}{\mathrm{O}}\left({{x}}^{{6}}\right)$ (1)
 > $r≔\mathrm{powdiff}\left(s\right):$
 > $\mathrm{tpsform}\left(r,x,10\right)$
 ${1}{-}{x}{+}{{x}}^{{2}}{-}{{x}}^{{3}}{+}{{x}}^{{4}}{-}{{x}}^{{5}}{+}{{x}}^{{6}}{-}{{x}}^{{7}}{+}{{x}}^{{8}}{-}{{x}}^{{9}}{+}{\mathrm{O}}\left({{x}}^{{10}}\right)$ (2)