# Derivative of generating function (Example from documentation)

Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later. Fixed in 13.2.0 or earlier.

In the documentation for GeneratingFunction, the following example is given under Examples -> Properties & Relations -> Derivative:

GeneratingFunction[n f[n], n, z]
(*z (GeneratingFunction^(0,0,1))[f[n],n,z]*)


When I evaluate the input, however, I obtain something different, namely:

GeneratingFunction[n f[n], n, z]
(*z GeneratingFunction[(1 + n) f[1 + n], n, z]*)


For me the first output would be preferable; indeed I would like Mathematica to express any expression of the form

GeneratingFunction[p[n] f[n], n, z] (*p[n] an explicit polynomial in n*)


in terms of derivatives of the generating function of the sequence f[n]. I think this is the intended behaviour of GeneratingFunction and certainly what I remember from v8.

Question: Is there a way to achieve this behaviour?

I am currently using version 9.0 on a 64bit Linux computer.

• Same in 9.0.1 Windows. ZTransform behavior similarly changed it appears.
– ciao
Apr 12, 2014 at 22:28
• The issue persists in the Raspberry Edition of Mma v10. Apr 19, 2014 at 19:20
• This is a bug either of the function or of the documentation. I have tagged it accordingly. Whether the change in behavior was intentional or not I cannot say. Aug 18, 2014 at 23:22