New proofs of some double sum Rogers–Ramanujan type identities

Multidimensional Rogers-Ramanujan type identities with parameters

“…The sum of (1.6) and (4.3) creates j, k≥0 q 4j 2 +4jk+2k 2 +k (q; q) 2j (q 2 ; q 2 ) k x 2j+2k = 1 2 (−qx; q) ∞ + (qx; q) ∞ . (−q; q 2 ) ∞ + (q; q 2 ) ∞ = 2 (q 4 ; q 4 ) ∞ (q 16 , −q 6 , −q 10 ; q 16 ) ∞ . (4.5)…”

“…Though the contour integral method, Wang [16] recovered (1.3) and (1.4) and Cao and Wang [6,Theorem 3.8] found the following two formulas:…”