Geodesic
Inversion of bilateral basic hypergeometric series
The electronic journal of combinatorics, Tome 10 (2003)

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Zbl arXiv EuDML
We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is 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. We combine our bilateral matrix inverse with known basic hypergeometric summation theorems to derive, via inverse relations, several new identities for bilateral basic hypergeometric series.
DOI : 10.37236/1703
Classification : 33D15, 15A09
Mots-clés : bilateral basic hypergeometric series, bilateral matrix inverses, Bailey's very-well-poised summation formula 
Michael Schlosser. Inversion of bilateral basic hypergeometric series. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1703
@article{10_37236_1703,
     author = {Michael Schlosser},
     title = {Inversion of bilateral basic hypergeometric series},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1703},
     zbl = {1022.33010},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1703/}
}
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