IsHypergeometricTerm - Maple Help

RationalNormalForms

 IsHypergeometricTerm
 test if a given expression is a hypergeometric term

 Calling Sequence IsHypergeometricTerm(H, n, certificate)

Parameters

 H - expression in n n - variable certificate - (optional) name

Description

 • The IsHypergeometricTerm(H,n) function returns true if $H\left(n\right)$ is a hypergeometric term in n. Otherwise, false is returned.
 An expression H is hypergeometric in n if $\frac{H\left(n+1\right)}{H\left(n\right)}=R\left(n\right)$, a rational function in n. $R\left(n\right)$ is the certificate of $H\left(n\right)$.
 • If the third optional argument is included, it is assigned to the certificate of $H\left(n\right)$.
 • This function is part of the RationalNormalForms package, and so it can be used in the form IsHypergeometricTerm(..) only after executing the command with(RationalNormalForms). However, it can always be accessed through the long form of the command by using RationalNormalForms[IsHypergeometricTerm](..).

Examples

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