termscale - Maple Help

genfunc

 termscale
 determine the result of multiplying a generating function by a polynomial

 Calling Sequence termscale(pz, z, fn, n)

Parameters

 pz - polynomial in z z - name, polynomial variable fn - expression for the nth term in a sequence n - name, index variable for fn

Description

 • This function shifts and scales fn to determine the sequence encoded by the product of pz and the generating function of fn.
 • The command with(genfunc,termscale) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{genfunc}\right):$
 > $\mathrm{termscale}\left(1+az,z,n{2}^{n}t\left(n\right)+{n}^{2}t\left(n-1\right),n\right)$
 ${a}{}\left(\left({n}{-}{1}\right){}{{2}}^{{n}{-}{1}}{}{t}{}\left({n}{-}{1}\right){+}{\left({n}{-}{1}\right)}^{{2}}{}{t}{}\left({n}{-}{2}\right)\right){+}{n}{}{{2}}^{{n}}{}{t}{}\left({n}\right){+}{{n}}^{{2}}{}{t}{}\left({n}{-}{1}\right)$ (1)