Guessing at the size (I'm thinking about 1/2" wide or so), I think that an epoxy product would be your best best. I had a similar gap on the apron of my driveway that I filled with Rustoleum EpoxyShield concrete repair mixed with sand and it's held up fine for 3 years now. It's a two part epoxy and the sand stretches it a bit further, gives it some binder, and thickens it so you can trowel it. IIRC it was ~$20 at the local HD. As with any epoxy concrete junction, you should clean out the **** that collects in the gap over the years and maybe grind the margins for the best adhesion. One caveat...I don't do this for a living, just a guy doing what needs to be done to keep the house maintained, so I may be totally off base. <- standard disclaimer.
