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arXiv · 2412.03559

A family of orthogonal functions on the unit circle and a new multilateral matrix inverse

Michael J. Schlosser
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Abstract

Using Bailey's very-well-poised $_6\psi_6$ summation, we show that a specific sequence of well-poised bilateral basic hypergeometric $_3\psi_3$ series form a family of orthogonal functions on the unit circle. We further extract a bilateral matrix inverse from Dougall's ${}_2H_2$ summation which we use, in combination with the Pfaff--Saalsch\"utz summation, to derive a summation for a particular bilateral hypergeometric $_3H_3$ series. We finally provide multivariate extensions of the bilateral matrix inverse and the $_3H_3$ summation in the setting of hypergeometric series associated to the root system $A_r$.

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Michael J. Schlosser. 2024-12-04. A family of orthogonal functions on the unit circle and a new multilateral matrix inverse. https://arxiv.org/abs/2412.03559

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