By using a certain q-Stirling approximation, we show that the convergence region for the second q-Appell function Φ2 is formally decided by a certain Nalli-Ward-AlSalam (NWA) q-addition. The convergence region for Φ1 is the same as for q = 1. In the process we investigate numerical aspects, including an absolute maximum, of the NWA q-addition of two letters.