Michael J. Schlosser
Multilateral inversion of Ar,
Cr and Dr
basic hypergeometric series
(24 pages)
Abstract.
In [Electron. J. Combin. 10 (2003), #R10], the author
presented a new basic hypergeometric matrix inverse with applications
to bilateral basic hypergeometric series. This matrix inversion result
was directly extracted from an instance of Bailey's very-well-poised
6Ψ6 summation theorem, and involves two
infinite matrices
which are not lower-triangular. The present paper features three
different multivariable generalizations of the above result.
These are extracted from Gustafson's Ar and
Cr extensions and of the author's recent
Ar extension of Bailey's
6Ψ6 summation formula. By combining
these new multidimensional matrix inverses with Ar
and Dr extensions of Jackson's
8Φ7 summation
theorem three balanced very-well-poised
8Ψ8 summation theorems associated
with the root systems Ar and Cr
are derived.
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