On a 3-Way Combinatorial Identity

Recently in [1] Goyal and Agarwal interpreted a generalized basic series as a generating function for a colour partition function and a weighted lattice path function. This led to an infinite family of combinatorial identities. Using Frobenius partitions, we in this paper extend the result of [1] and obtain an infinite family of 3-way combinatorial identities. We illustrate by an example that our main result has a potential of yielding Rogers-Ramanujan-MacMahon type identities with convolution property.