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genfunc

  

rgf_relate

  

relate sequences with common factors in their generating functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

rgf_relate(Fz, z, Fn, n, Gz)

rgf_relate(Fz, z, Fn, n, Gy, y)

Parameters

Fz

-

rational generating function

z

-

name, generating function variable

Fn

-

expression for nth term of the sequence encoded by Fz

n

-

name, index variable for Fn

Gz, Gy

-

rational generating function

y

-

(optional) name, generating function variable for Gy

Description

• 

This function relates sequences with common nonzero roots in the denominators of their generating functions. If the generating functions do not have common roots, FAIL is returned.

• 

If the optional parameter y is used, it is the generating function variable for the fifth parameter. The generating function Gy must not involve the variable z in this case.

• 

The nth term of the sequence encoded by Gz (Gy) is expressed as a function of Fn.

• 

The value FAIL is returned if Fz is a trivial rational generating function.

• 

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

Examples

withgenfunc:

Fz11az1bz:

rgf_relateFz,z,fn,n,11az

bfn1+fn

(1)

rgf_relate11bz,z,gn,n,Fz

bgnab+aanab

(2)

rgf_relateFz,z,fn,n,11bw1cw,w

bafn1bc+bfnbcccnbc

(3)

rgf_relateFz,z,fn,n,11az2

bn+1fn1+n+1fn

(4)

normal

nbfn1bfn1+nfn+fn

(5)

Fzz1zz2:

rgf_relateFz,z,Fn,n,Fz2

15n15Fn+25nFn1

(6)

normal

15Fnn15Fn+25nFn1

(7)

See Also

genfunc

genfunc/rgf_charseq

 


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