powseries - Maple Programming Help

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powseries

 powsqrt
 square root of an expression as a power series

 Calling Sequence powsqrt(p)

Parameters

 p - formal power series, polynomial, or any function that is acceptable for power series package

Description

 • The function powsqrt(p) returns the formal power series that is the square root of p.
 • The power series of p must have a nonzero first term ($p\left(0\right)\ne 0$) for its logarithm to be well-defined.
 • The command with(powseries,powsqrt) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{powseries}\right):$
 > $s≔\mathrm{powsqrt}\left({x}^{2}+x+1\right):$
 > $\mathrm{tpsform}\left(s,x,7\right)$
 ${1}{+}\frac{{1}}{{2}}{}{x}{+}\frac{{3}}{{8}}{}{{x}}^{{2}}{-}\frac{{3}}{{16}}{}{{x}}^{{3}}{+}\frac{{3}}{{128}}{}{{x}}^{{4}}{+}\frac{{15}}{{256}}{}{{x}}^{{5}}{-}\frac{{57}}{{1024}}{}{{x}}^{{6}}{+}{\mathrm{O}}\left({{x}}^{{7}}\right)$ (1)
 > $t≔\mathrm{powsqrt}\left({ⅇ}^{x}\right):$
 > $\mathrm{tpsform}\left(t,x,5\right)$
 ${1}{+}\frac{{1}}{{2}}{}{x}{+}\frac{{1}}{{8}}{}{{x}}^{{2}}{+}\frac{{1}}{{48}}{}{{x}}^{{3}}{+}\frac{{1}}{{384}}{}{{x}}^{{4}}{+}{\mathrm{O}}\left({{x}}^{{5}}\right)$ (2)
 > $\mathrm{tpsform}\left(\mathrm{powsqrt}\left(\mathrm{powdiff}\left(\mathrm{powlog}\left(1+x\right)\right)\right),x,5\right)$
 ${1}{-}\frac{{1}}{{2}}{}{x}{+}\frac{{3}}{{8}}{}{{x}}^{{2}}{-}\frac{{5}}{{16}}{}{{x}}^{{3}}{+}\frac{{35}}{{128}}{}{{x}}^{{4}}{+}{\mathrm{O}}\left({{x}}^{{5}}\right)$ (3)