The listtohypergeom(l, x, [typelist]) command computes a $\mathrm{2F1}$ hypergeometric series in x for the generating function of the expressions in l.  This generating function has its type specified by typelist, for example, ordinary (ogf) or exponential (egf). For a complete list of available generating function types, see gftypes.

You should specify at least 6 terms in the list l.

The seriestohypergeom(s, x, [typelist]) command computes a $\mathrm{2F1}$ hypergeometric series in x for the generating function of the expressions in s.  This generating function has its type specified by typelist, for example, ordinary (ogf) or exponential (egf). For a complete list of available generating function types, see gftypes.

You should specify at least 6 terms in the series s.

If typelist contains more than one element, these types are considered in the order that they are listed.

If typelist is not specified, the default typelist, 'ogf','egf', is used.

The function returns a list whose first element is the hypergeometric function. The second element is the generating function type for which an equation was found.

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

$l≔\left[1\,2\,5\,14\,42\,132\,429\,1430\right]$

$l≔\left[1\,2\,5\,14\,42\,132\,429\,1430\right]$

$\mathrm{listtohypergeom}\left(l\,x\right)$

$\left[\frac{4}{{\left(1+\sqrt{1-4x}\right)}^2}\,\mathrm{ogf}\right]$

$\mathrm{seriestohypergeom}\left(\mathrm{series}\left(1+2x+5x^2+14x^3+42x^4+132x^5+429x^6+1430x^7\,x\,8\right)\right)$

$\left[\frac{4}{{\left(1+\sqrt{1-4x}\right)}^2}\,\mathrm{ogf}\right]$