Some More Identities of Kanade–Russell Type Derived Using Rosengren’s Method

Multi-sum Rogers-Ramanujan Type Identities

“…Recently, Mc Laughlin [20] applied Rosengren's method in [25] to derive some new Rogers-Ramanujan type identities including the following one of index (1,2,3) i,j,k≥0 (−1) j q (3k+2j−i)(3k+2j−i−1)/2+j(j−1)−i+6j+6k (q; q) i (q 2 ; q 2 ) j (q 3 ; q 3 ) k = (−1; q) ∞ (q 18 ; q 18 ) ∞ (q 3 ; q 3 ) ∞ (q 9 ; q 18 ) ∞ .…”

“…Note that in [20], such identities are called as identities of Kanade-Russell type. In the way of finding generalizations of Capparelli's first partition identity, Dousse and Lovejoy [13,Eqs. (2.6),(2.7)] proved the following identity of index (1, 1, 1, 2):…”