SumTools[Hypergeometric] - Maple Programming Help

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SumTools[Hypergeometric]

 IsHypergeometricTerm
 test if a given expression is a hypergeometric term

 Calling Sequence IsHypergeometricTerm(H, n, certificate)

Parameters

 H - function of n n - variable certificate - (optional) name; assigned the computed certificate

Description

 • The IsHypergeometricTerm(H,n) command returns true if $H\left(n\right)$ is a hypergeometric term of n. Otherwise, it returns false.
 A function H is hypergeometric of n if $\frac{H\left(n+1\right)}{H\left(n\right)}=R\left(n\right)$, a rational function of n. $R\left(n\right)$ is the certificate of $H\left(n\right)$. If the third optional argument is included, it is assigned the certificate $R\left(n\right)$.

Examples

 > $\mathrm{with}\left(\mathrm{SumTools}[\mathrm{Hypergeometric}]\right):$
 > $H≔\frac{\left({n}^{2}-1\right)\left(3n+1\right)!}{\left(n+3\right)!\left(2n+7\right)!}$
 ${H}{≔}\frac{\left({{n}}^{{2}}{-}{1}\right){}\left({3}{}{n}{+}{1}\right){!}}{\left({n}{+}{3}\right){!}{}\left({2}{}{n}{+}{7}\right){!}}$ (1)
 > $\mathrm{IsHypergeometricTerm}\left(H,n,'\mathrm{certificate}'\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{certificate}$
 $\frac{{3}}{{2}}{}\frac{\left({3}{}{n}{+}{2}\right){}\left({3}{}{n}{+}{4}\right){}{n}{}\left({n}{+}{2}\right)}{\left({n}{-}{1}\right){}\left({2}{}{n}{+}{9}\right){}{\left({n}{+}{4}\right)}^{{2}}}$ (3)