Michael J. Schlosser
A family of orthogonal functions on the unit circle and a new multilateral matrix inverse
(16 pages)
Abstract.
Using Bailey's very-well-poised 6Ψ6
summation, we show that a specific sequence of well-poised bilateral
basic hypergeometric 3Ψ3 series form a
family of orthogonal functions on the unit circle.
We further extract a bilateral matrix inverse from
Dougall's 2H2 summation which we use,
in combination with the Pfaff-Saalschütz summation,
to derive a summation for a particular bilateral
hypergeometric 3H3 series.
We finally provide multivariate extensions of the bilateral
matrix inverse and the 3H3 summation
in the setting of hypergeometric series associated to the root
system Ar.
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