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Multiple Expansion Formulas over Root Systems

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Abstract

In this paper, we deduce several multiple expansion formulas over root systems. These formulas give some multiple extensions of an expansion formula of Liu. From these formulas, we establish multiple expansion formulas for infinite products, a \(C_{n}\) extension of Rogers’ non-terminating \(\text {}_{6}\phi _{5}\) summation formula and multiple expansion formulas for \((q)_{\infty }^{m}.\) As applications, we deduce several \(C_{n}\) and \(D_{n}\) extensions of finite/semi-finite forms of the quintuple product identity, a multiple extension of an expansion formula of Liu and a \(C_{n}\) extension of Liu’s extension of Rogers’ \(\text {}_{6}\phi _{5}\) summation formula.

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Funding

This work was partially supported by the Natural Science Foundation of Changsha (Grant No. kq2208251).

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  1. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Bing He & Suzhen Wen

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  1. Bing He
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  2. Suzhen Wen
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He, B., Wen, S. Multiple Expansion Formulas over Root Systems. Results Math 79, 33 (2024). https://doi.org/10.1007/s00025-023-02053-8

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