The AreSimilar(S,T,n) function returns true if $S\left(n\right)$ and $T\left(n\right)$ are similar. Otherwise, false is returned.

Two hypergeometric terms $S\left(n\right)$ and $T\left(n\right)$ are similar if their ratio is a rational function of n.

This function is part of the RationalNormalForms package, and so it can be used in the form AreSimilar(..) only after executing the command with(RationalNormalForms). However, it can always be accessed through the long form of the command by using RationalNormalForms[AreSimilar](..).

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

$\mathrm{S1}≔n^2\;$$\mathrm{S2}≔2^n\;$$T≔1$

$\mathrm{S1}≔n^2$

$\mathrm{S2}≔2^n$

$T≔1$

$\mathrm{AreSimilar}\left(\mathrm{S1}\,T\,n\right)$

$\mathrm{true}$

$\mathrm{AreSimilar}\left(\mathrm{S2}\,T\,n\right)$

$\mathrm{false}$

$\mathrm{T1}≔\frac{1}{\left(n+3\right)!\left(2n+7\right)!}\left(3n+1\right)!$

$\mathrm{T1}≔\frac{\left(3n+1\right)!}{\left(n+3\right)!\left(2n+7\right)!}$

$\mathrm{T2}≔\frac{\left(n^2-1\right)\left(3n+1\right)!}{\left(n+3\right)!\left(2n+7\right)!}$

$\mathrm{T2}≔\frac{\left(n^2-1\right)\left(3n+1\right)!}{\left(n+3\right)!\left(2n+7\right)!}$

$\mathrm{AreSimilar}\left(\mathrm{T1}\,\mathrm{T2}\,n\right)$

$\mathrm{true}$