2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79077A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.18 pages, AMSLaTeXQuantum AlgebraCombinatorics33D15; 05A30; 05A10text