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genfunc

 rgf_hybrid
 Find generating function of hybrid terms

 Calling Sequence rgf_hybrid(z, gf1, gf2, ...)

Parameters

 z - name, generating function variable gf1, gf2, ... - one or more rational generating functions

Description

 • This procedure finds the generating function of the hybrid terms that results from the term wise multiplication of the sequences encoded by the generating functions gf1, gf2, ....
 • The command with(genfunc,rgf_hybrid) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{genfunc}\right):$
 > $\mathrm{rgf_hybrid}\left(z,\frac{1}{1-2z},\frac{2z}{1-3z}\right)$
 ${-}\frac{{4}{}{z}}{{6}{}{z}{-}{1}}$ (1)
 > $\mathrm{rgf_hybrid}\left(z,\frac{z}{1-z-{z}^{2}},\frac{1}{1-2z}\right)$
 ${-}\frac{{2}{}{z}}{{4}{}{{z}}^{{2}}{+}{2}{}{z}{-}{1}}$ (2)
 > $\mathrm{pz}≔\mathrm{rgf_encode}\left(n,n,z\right)$
 ${\mathrm{pz}}{:=}\frac{{z}}{{\left({1}{-}{z}\right)}^{{2}}}$ (3)
 > $\mathrm{fz}≔\mathrm{rgf_hybrid}\left(z,\mathrm{pz},\mathrm{pz}\right)$
 ${\mathrm{fz}}{:=}{-}\frac{{{z}}^{{2}}{+}{z}}{{{z}}^{{3}}{-}{3}{}{{z}}^{{2}}{+}{3}{}{z}{-}{1}}$ (4)
 > $\mathrm{normal}\left(\mathrm{rgf_expand}\left(\mathrm{fz},z,n\right)\right)$
 ${{n}}^{{2}}$ (5)