Balanced3ϕ2Summation Theorems forU(n) Basic Hypergeometric Series

Elementary derivations of identities for bilateral basic hypergeometric series

“…We expect that our technique will allow one to proceed from lower level identities to systematically derive the upper level ones. In particular, we plan to apply the methods of this article and of [33] in the setting of multiple basic hypergeometric series associated to root systems, see e.g., Milne [29], Gustafson [18], v. Diejen [13], and Schlosser [32].…”

Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem

“…Proposition 3.1 (The nonterminating U(n + 1) refinement of the q-binomial theorem, Theorem 5.42 of [10]). Let b, z and x 1 , .…”

A new multivariable 6 ψ 6 summation formula

“…. , r, case of [25], Lemma 3.12, specifically (6.4) to transform the expression obtained in (6.3) to (aq, q/a, aq/bd) ∞ (aq/C, aq 1+|m| /bCd, q 1+|m| /a) ∞ r i,j =1 (qx i /x j , q 1+m j x i /c i x j ) ∞ (qx i /c i x j , q 1+m j x i /x j ) ∞ × r i=1 (x i q 1+|m| /d, q 1+m i /bx i , aq/bCx i , ax i q/c i d) ∞ (x i q 1+|m|−m i /d, q/bx i , ax i q/d, ac i q/bCx i ) ∞ , which is exactly the 1/e i = q m i /a, i = 1, . .…”