AreSimilar - Maple Help

SumTools[Hypergeometric]

 AreSimilar
 test if two hypergeometric terms are similar

 Calling Sequence AreSimilar(S, T, n)

Parameters

 S - hypergeometric term of n T - hypergeometric term of n n - variable

Description

 • The AreSimilar(S,T,n) command returns true if $S\left(n\right)$ and $T\left(n\right)$ are similar. Otherwise, it returns false.
 Two hypergeometric terms $S\left(n\right)$ and $T\left(n\right)$ are similar if their ratio is a rational function of n.

Examples

 > $\mathrm{with}\left(\mathrm{SumTools}\left[\mathrm{Hypergeometric}\right]\right):$
 > $\mathrm{S1}≔{n}^{2};$$\mathrm{S2}≔{2}^{n};$$T≔1$
 ${\mathrm{S1}}{≔}{{n}}^{{2}}$
 ${\mathrm{S2}}{≔}{{2}}^{{n}}$
 ${T}{≔}{1}$ (1)
 > $\mathrm{AreSimilar}\left(\mathrm{S1},T,n\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{AreSimilar}\left(\mathrm{S2},T,n\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{T1}≔\frac{1}{\left(n+3\right)!\left(2n+7\right)!}\left(3n+1\right)!$
 ${\mathrm{T1}}{≔}\frac{\left({3}{}{n}{+}{1}\right){!}}{\left({n}{+}{3}\right){!}{}\left({2}{}{n}{+}{7}\right){!}}$ (4)
 > $\mathrm{T2}≔\frac{\left({n}^{2}-1\right)\left(3n+1\right)!}{\left(n+3\right)!\left(2n+7\right)!}$
 ${\mathrm{T2}}{≔}\frac{\left({{n}}^{{2}}{-}{1}\right){}\left({3}{}{n}{+}{1}\right){!}}{\left({n}{+}{3}\right){!}{}\left({2}{}{n}{+}{7}\right){!}}$ (5)
 > $\mathrm{AreSimilar}\left(\mathrm{T1},\mathrm{T2},n\right)$
 ${\mathrm{true}}$ (6)