iPhone 5S update to IOS8
This can help someone :
During the update ( Backup then update ) via iTunes from MacBook Air the iPhone 5S did not respond for a few hours , only Apple logo on the screen.
I used all method described :
try to switch off = no change , the logo is still on screen
reset several times ( Home+Power more than 10 sec ) = the phone switch off and after start the same logo
connect to Mac holding down home button = after start the same logo
Note that the iTunes does not detect the iPhone.
I put my shoes to go to Apple service but I had a last try : Home+Volume+Power and voila iTunes detected the phone , started the recovery and now it works .
It seems that Apple did not documented that Home+Volume+Power sequence.