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powseries

 inverse
 multiplicative inverse of a formal power series

 Calling Sequence inverse(p)

Parameters

 p - formal power series

Description

 • The function inverse(p) returns a formal power series that is the inverse of p with respect to multiply.
 • That is, multiply(p, inverse(p)) will return the formal power series equivalent to 1.
 • The command with(powseries,inverse) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $\mathrm{powcreate}\left(t\left(n\right)=\frac{t\left(n-1\right)}{n},t\left(0\right)=1\right):$
 > $s≔\mathrm{inverse}\left(t\right):$
 > $\mathrm{tpsform}\left(s,x,7\right)$
 ${1}{-}{x}{+}\frac{{1}}{{2}}{}{{x}}^{{2}}{-}\frac{{1}}{{6}}{}{{x}}^{{3}}{+}\frac{{1}}{{24}}{}{{x}}^{{4}}{-}\frac{{1}}{{120}}{}{{x}}^{{5}}{+}\frac{{1}}{{720}}{}{{x}}^{{6}}{+}{\mathrm{O}}\left({{x}}^{{7}}\right)$ (1)