During i OS update, you have to put i Phone into recovery mode, which may cause a restart-loop or i Phone gets stuck on red i Tunes logo, especially when not done properly.
If you think the update is stuck, press one of the buttons.
If you see an updating message, the update is still in progress.
If you're updating over the air, connect your device to a power source so that it won't run out of power during this process.
If your device runs out of power, connect it to a power source and turn on the device to let the update or restore complete.
I'm afraid you have to repair the i OS operating system to get your frozen i Phone back to normal.