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genfunc[rgf_expand] - expand rational generating functions

Calling Sequence

rgf_expand(Fz, z, n)

Parameters

Fz

-

rational generating function of z

z

-

name, the generating function variable

n

-

name, the index variable for the expansion of Fz

Description

• 

The function finds the closed form expansion of the nth term in the sequence encoded by the rational generating function Fz.

• 

If the denominator of Fz has polynomial factors of degree greater than two that cannot be factored over the rationals, an inert Sum expression involving RootOf values is returned.

• 

The global variables _J and _R are used in the RootOf expressions.

• 

The command with(genfunc,rgf_expand) allows the use of the abbreviated form of this command.

Examples

withgenfunc:

rgf_expand115z+6z2,z,n

22n+33n

(1)

rgf_expandy1yy2,y,k

1551525+1k5+115525+1k

(2)

rgf_expand1+2z+3z21zz2z3,z,n

_R=RootOf_Z3+_Z2+_Z1limz→_Rz_R3z2+2z+1z3+z2+z11_Rn_R

(3)

See Also

genfunc, genfunc/rgf_encode, invztrans, RootOf, ztrans


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