listtohypergeom - Maple Help

gfun

 listtohypergeom
 find a hypergeometric generating function
 seriestohypergeom
 find a hypergeometric generating function

 Calling Sequence listtohypergeom(l, x, [typelist]) seriestohypergeom(s, [typelist])

Parameters

 l - list x - name; variable name typelist - (optional) list of generating function types. The default is 'ogf','egf'. For a complete list of types, see gftypes. s - series

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{gfun}\right):$
 > $l≔\left[1,2,5,14,42,132,429,1430\right]$
 ${l}{≔}\left[{1}{,}{2}{,}{5}{,}{14}{,}{42}{,}{132}{,}{429}{,}{1430}\right]$ (1)
 > $\mathrm{listtohypergeom}\left(l,x\right)$
 $\left[\frac{{4}}{{\left({1}{+}\sqrt{{1}{-}{4}{}{x}}\right)}^{{2}}}{,}{\mathrm{ogf}}\right]$ (2)
 > $\mathrm{seriestohypergeom}\left(\mathrm{series}\left(1+2x+5{x}^{2}+14{x}^{3}+42{x}^{4}+132{x}^{5}+429{x}^{6}+1430{x}^{7},x,8\right)\right)$
 $\left[\frac{{4}}{{\left({1}{+}\sqrt{{1}{-}{4}{}{x}}\right)}^{{2}}}{,}{\mathrm{ogf}}\right]$ (3)