The function multiply(a, b) returns the formal power series that is the product of a and b.

The command with(powseries,multiply) allows the use of the abbreviated form of this command.

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

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

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

$s≔\mathrm{multiply}\left(t\,v\right)\:$

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

$1+\frac{3}{2}x+\frac{5}{4}{x}^2+\frac{19}{24}{x}^3+\frac{7}{16}{x}^4+\frac{109}{480}{x}^5+O\left(x^6\right)$