Variants of classical q-hypergeometric identities and partition implications

Utilizing a six-variable extension of Heine’s q-hypergeometric transformation that we previously obtained, we now derive variants of Heine’s transformation formula and the Lebesgue identity. The variant of Cauchy’s identity also obtained by us earlier is crucial in these derivations. We then establish some new partition identities which are variants of, and shed new light on, some fundamental classical partition identities.