Multiple Expansion Formulas over Root Systems.

In this paper, we deduce several multiple expansion formulas over root systems. These formulas give some multiple extensions of an expansion formula of Liu. From these formulas, we establish multiple expansion formulas for infinite products, a C n extension of Rogers’ non-terminating 6 ϕ 5 summation formula and multiple expansion formulas for (q) ∞ m. As applications, we deduce several C n and D n extensions of finite/semi-finite forms of the quintuple product identity, a multiple extension of an expansion formula of Liu and a C n extension of Liu’s extension of Rogers’ 6 ϕ 5 summation formula. [ABSTRACT FROM AUTHOR]