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Multilateral Inversion of A r , C r , and D r Basic Hypergeometric Series

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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 A r and C r extensions and from the author’s recent A r extension of Bailey’s 6ψ6 summation formula. By combining these new multidimensional matrix inverses with A r and D r extensions of Jackson’s 8ϕ7 summation theorem three balanced verywell- poised 8ψ8 summation theorems associated to the root systems A r and C r are derived.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A-1090, Vienna, Austria

    Michael J. Schlosser

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  1. Michael J. Schlosser
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Correspondence to Michael J. Schlosser.

Additional information

Partly supported by FWF Austrian Science Fund grants P17563-N13, and S9607 (the second is part of the Austrian National Research Network “Analytic Combinatorics and Probabilistic Number Theory”).

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Schlosser, M.J. Multilateral Inversion of A r , C r , and D r Basic Hypergeometric Series. Ann. Comb. 13, 341–363 (2009). https://doi.org/10.1007/s00026-009-0026-9

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