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genfunc

  

rgf_expand

  

expand rational generating functions

 

Calling Sequence

Parameters

Description

Examples

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

33n22n

(1)

rgf_expandy1yy2,y,k

15525+1k1551525+1k5+1

(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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