A multidimensional generalization of Shukla's 8-psi-8 summation
Classical Analysis and ODEs
2019-02-22 v1 Combinatorics
Quantum Algebra
Abstract
We give an r-dimensional generalization of H. S. Shukla's very-well-poised 8-psi-8 summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system A_{r-1}, or equivalently, the unitary group U(r). Our proof, which is already new in the one-dimensional case, utilizes an A_{r-1} nonterminating very-well-poised 6-phi-5 summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.
Cite
@article{arxiv.math/0103024,
title = {A multidimensional generalization of Shukla's 8-psi-8 summation},
author = {Michael Schlosser},
journal= {arXiv preprint arXiv:math/0103024},
year = {2019}
}
Comments
16 pages, AMS-LaTeX