# What is the Maclaurin series of z^3sin(z^2)

What is the Maclaurin series of
${z}^{3}\mathrm{sin}\left({z}^{2}\right)$
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Kenley Rasmussen
Recall that
$\mathrm{sin}\left(z\right)=\sum _{n=0}^{\mathrm{\infty }}\frac{\left(-1{\right)}^{n}{z}^{2n+1}}{\left(2n+1\right)!}$
Thus,
$\mathrm{sin}\left({z}^{2}\right)=\sum _{n=0}^{\mathrm{\infty }}\frac{\left(-1{\right)}^{n}{z}^{4n+2}}{\left(2n+1\right)!}$
and finally
${z}^{3}\mathrm{sin}\left({z}^{2}\right)=\sum _{n=0}^{\mathrm{\infty }}\frac{\left(-1{\right)}^{n}{z}^{4n+5}}{\left(2n+1\right)!}$