Beside fari (to do), grammars like this one give six other forms of the infinitive in Esperanto:
simple / progressive / perfect / prospective
(active) fari esti faranta / esti farinta / esti faronta
(passive) ??? esti farata / esti farita / esti farota
But I can't find the passive equivalent to fari: is it something like esti fari?
Any help would be appreciated!
It is all very simple, there is a marvellous Esperanto middle voice derivational suffix -iĝ- which makes every root passive (at least from the point of view of an English speaker). Followed by the infinitive suffix -i (-iĝi) it forms passive infinitives:
fari - "to do/make"
fariĝi - "to be done/made"
Note, that making passives with this suffix lies in the sphere of derivation, word building, and not in the sphere of conjugation, that can be the reason you haven't at once remembered about it as a passive suffix.
Any Esperanto adjectival root can be turned into a verb of state by simply adding the verbal endings. This gives rise to another class of passive infinitives derived from passive participles:
Passive Participle Derived Infinitive Meaning
------------------ ------------------ -------
farita fariti to have been done
farata farati to be in the process or state of being done
farota faroti to be done sometime in the future
Because passive participial suffixes are unavoidably temporal, you can't create intemporal passive infinitives this way (for that, use fariĝi suggested above).
As an aside, you can, of course, do the same thing with active participles to create a series of temporal active infinitives:
Active Participle Derived Infinitive Meaning
----------------- ------------------ -------
farinta farinti to have done
faranta faranti to be doing
faronta faronti to be about to do, to be going to do
