Recently, H. M. Srivastava extended certain interesting generating functions of L. Carlitz to the forms:
![](//static-cambridge-org.ezproxyberklee.flo.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0008439500065127/resource/name/S0008439500065127_eqn1.gif?pub-status=live)
and
![](//static-cambridge-org.ezproxyberklee.flo.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0008439500065127/resource/name/S0008439500065127_eqn2.gif?pub-status=live)
where
are general oncand many-parameter sequences of functions. In the present paper some general addition formulas for analogous sequences of functions are derived, and a number of interesting applications of the main results are given.