Finding general difference polynomials' recurrance relation

[jsdf]

Hi!

I have a sequence of difference polynomials (which I obtained by the method of finite differences) and I would like to find out if there is a recurrence relation between them.



The generating function of general difference polynomials is given by:

How would one write the above using maple and is there a way to find out in maple if there exists a recurrence relation between those polynomials?

 

[lippyka]

Yes, it is possible to use Maple to find out if there is a recurrence relation between difference polynomials. To do this, you will need to use the `algcurves` package. This package provides a set of commands which can be used to work with algebraic curves and their associated difference equations. To use the package, you will first need to load it:with(algcurves):Once the package is loaded, you can write your difference polynomials in the form:dP[n] = a0 + a1*n^2 + a2*n^4 + ...where dP[n] is the difference polynomial for the nth term. You can then use the command `recurrence` to find a recurrence relation for the polynomials. For example, the following command will search for a recurrence relation for the polynomials dP[n]:recurrence(dP[n]);The command will return the recurrence relation, if one exists. I hope this helps!