Abstract
Three new summation formulas for 6 ψ 6 bilateral basic hypergeometric series attached to root systems are presented. Remarkably, two of these formulae, labelled by the A2n−1 and A2n root systems, can be reduced to multiple 6 φ 5 sums generalising the well-known van Diejen sum. This latter sum serves as the weight-function normalisation for the BC n q-Racah polynomials of van Diejen and Stokman. Two 8 φ 7-level extensions of the multiple 6 φ 5 sums, as well as their elliptic analogues, are conjectured. This opens up the prospect of constructing novel A-type extensions of the Koornwinder–Macdonald theory.
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