gfun[listtohypergeom] - find an hypergeometric generating function

gfun[seriestohypergeom] - find an hypergeometric generating function

listtohypergeom(l, x, <[typelist]>)

seriestohypergeom(s, <[typelist])

l - a list

s - a series

x - the unknown variable

[typelist] - (optional) a list of generating function types

The procedures listtohypergeom and seriestohypergeom compute a 2F1 hypergeometric series in x for the generating function of the expressions in l or s. This generating function has its type specified by typelist, for example, ordinary (ogf) or exponential (egf). For a full list of available choices see gftypes).
If typelist contains more than one element, these types are tried in order.
If typelist is not provided, the default optionsgf=['ogf','egf'] is used. The output is a list whose second element is the type for which an equation was found, and whose first element is the hypergeometric function.
One should give at least 6 terms in the list l or the series s.

> with(gfun):
l:=[1,2,5,14,42,132,429,1430];

\[[1, 2, 5, 14, 42, 132, 429, 1430]\]

> listtohypergeom(l,x);

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

> seriestohypergeom(series(1+2*x+5*x^2+14*x^3+42*x^4+132*x^5+429*x^6+1430*x^7,x, 8));

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