Formal power series are procedures that return the coefficients of the power series they represent. Thus $\mathrm{name}\left(i\right)$ is the coefficient of $x^i$ in the series called name.

The values of the coefficients are saved using a remember table, so all computed coefficients can be seen via op(4, op(name)).

The actual procedure is identical for all power series; the only differences are the general term and the values that each remembers.

The general term of the power series can be obtained via name(_k) .

Note that each intermediate power series created in a calculation should be named.

$\mathrm{with}\left(\mathrm{powseries}\right)\:$

$\mathrm{powcreate}\left(e\left(n\right)=\frac{1}{n!}\,e\left(0\right)=1\right)\:$

$\mathrm{powcreate}\left(f\left(n\right)=\frac{f\left(n-1\right)}{n^{2}f\left(n-2\right)}\,f\left(0\right)=1\,f\left(1\right)=5\,f\left(2\right)=2\right)\:$

$\mathrm{tpsform}\left(e\,x\,6\right)$

$1+x+\frac{1}{2}{x}^2+\frac{1}{6}{x}^3+\frac{1}{24}{x}^4+\frac{1}{120}{x}^5+O\left(x^6\right)$

$\mathrm{tpsform}\left(f\,x\,6\right)$

$1+5x+2x^2+\frac{2}{45}{x}^3+\frac{1}{720}{x}^4+\frac{1}{800}{x}^5+O\left(x^6\right)$

$\mathrm{logf}≔\mathrm{powlog}\left(f\right)\:$

$\mathrm{elogf}≔\mathrm{multiply}\left(e\,\mathrm{logf}\right)\:$

$\mathrm{result}≔\mathrm{powexp}\left(\mathrm{elogf}\right)\:$

$\mathrm{tpsform}\left(\mathrm{result}\,x\,6\right)$

$1+5x+7x^2+\frac{767}{45}{x}^3+\frac{2351}{240}{x}^4+\frac{39231}{800}{x}^5+O\left(x^6\right)$