Best Power (motorized) Zoom Lens for the BMPCC!

I am looking for a Power or motorized zoom lens for my BMPCC.

I have been looking at this nice pancake, smaller sized Olympus M.ZUIKO Digital ED 14-42mm f3.5-5.6 EZ Lens.

Will the Motor, power zoom on this lens work with my BMPCC?

If not, does anyone have a list of power/motorized zoom lenses that will work with my camera?

Thanks!

EDIT: I just noticed that there is a Panasonic LUMIX G X Vario PZ 14-42mm that has a built in, physical on the lens, zoom switch. Will this work fine??

Yes, you will need a lens with the zoom control on the lens. The Olympus 13-50 EZ is the best power zoom MFT lens for video work, the others are mostly a still camera lens, requiring a lot of in-camera correction the Picket camera can not do. The Oly EZ lens uses the lens zoom ring to change the focal length (zoom in or out), a slight twist starts a slow zoom change, twist some more and the zoom speed increases, like the zoom rocker switch on a ENG zoom lens.

The other route, is to get a NTF or AbelCine B4 to MFT lens adapter, and get a B4 HD ENG zoom lens, this gives a large max f-stop that is constant, and true parfocal zoom focus, that holds the focus during a zoom change. But this is the most expensive route.

Another option, is going with a good manual zoom designed for video work, like the new Panasonic-Leica 12-60” zoom, which is not a power zoom, but has a nice smooth zoom control you can add a FF gear to and use a dampened Zoom control lever setup. The 12-60is dead silent in zoom and focus changes (another requirement for video work) and is also parfocal. This is the lens I went with, has very nice IQ and matches the other PL prime lenses in the lineup.
Cheers

Interesting Kim, thanks for the feedback. I have not used the Oly 12-50, going but previous feedback, it seemed the best MFT power zoom. I got the Penny Leica 12-60, and it is very nice.
Cheers