Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

Details Multilateral inversion of A_r, C_r and D_r basic hypergeometric series Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

2006-08-30

arxiv.org/abs/math/0608742v1

Mathematics

Classical Analysis and ODEs

24 pages

Scientific paper

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 6-psi-6 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 A_r and C_r extensions and of the author's recent A_r extension of Bailey's 6-psi-6 summation formula. By combining these new multidimensional matrix inverses with A_r and D_r extensions of Jackson's 8-phi-7 summation theorem three balanced very-well-poised 8-psi-8 summation theorems associated with the root systems A_r and C_r are derived.

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