find a recurrence for the elements - Maple Help

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gfun[listtorec] - find a recurrence for the elements

gfun[seriestorec] - find a recurrence for the coefficients of a series

Calling Sequence

listtorec(l, u(n), [typelist])

seriestorec(s, u(n), [typelist])

Parameters

l

-

list

u

-

name; function name

n

-

name; variable of the function u

typelist

-

(optional) list of generating function types. The default is 'ogf','egf'. For a complete list of types, see gftypes.

s

-

series

Description

• 

The listtorec(l, u(n), [typelist]) command computes a linear recurrence with polynomial coefficients satisfied by the expressions in l. A normalization is specified by typelist, for example, ordinary (ogf) or exponential (egf).  For a complete list of available generating function types, see gftypes.

• 

You should specify as many terms as possible in the list l.

• 

The seriestorec(s, u(n), [typelist]) command computes a linear recurrence with polynomial coefficients satisfied by the expressions in s. A normalization is specified by typelist, for example, ordinary (ogf) or exponential (egf).  For a complete list of available generating function types, see gftypes.

• 

You should specify as many terms as possible 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 a set containing the recurrence and its initial conditions.  The second element is the generating function type to which it corresponds.

Examples

withgfun:

l:=1,1,2,5,14,42,132,429,1430,4862,16796,58786:

rec:=listtorecl,un

rec:=4n6un+1+n+3un+2,u0=1,u1=1,ogf

(1)

rsolveop1,rec,un

4nΓn+12πΓn+2

(2)

rec2:=seriestorecseriesaddlixi1i1!,i=1..nopsl,x,12,un,'egf'

rec2:=4n6un+1+n+3un+2,u0=1,u1=1,egf

(3)

See Also

gfun, gfun/gftypes, gfun/parameters


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