My iphone 4 shows the apple logo for about 5 seconds then goes black and reapeats?

Yesterday I updated my iphone 4 but half way in the update I had to leave for school and brought the phone with me. When I got out of school I tried to turn my phone on but it keeps showing the apple logo for 5 seconds goes black and repeats when I don't even touch my phone. I try to plug my phone into my computer but it won't recognize my phone.

Hook up to itunes, hold power and home button util it get reconized, then restore.