Why there is no explanation and selection recommendation about C3 in dis picture taken from datasheet?
This can be found in other datasheets and other technical papers too. Please check using LT3959 datasheet page 17.
It is the section "Inverting Converter: Selecting the DC Coupling Capacitor".
AC or DC coupling?! I think their topology are different, becasuse as you can see in your case they have used coupled inductor!