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<p>We derive twenty different multivariable generalizations of Jackson’s <sub>2</sub><i>ϕ</i><sub>2</sub> transformation by applying elementary proofs. Then, by reversing the order of summation, we obtain eight multivariable extensions of transformations of terminating <sub>2</sub><i>ϕ</i><sub>1</sub> series. As limiting cases of our main results, we obtain three <i>A</i><sub><i>n</i></sub><sub>1</sub><i>ϕ</i><sub>1</sub> summation formulae.</p>

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Jackson’s 2ϕ2 transformations over the root systems An, Cn, Dn

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Pei Gao

摘要

We derive twenty different multivariable generalizations of Jackson’s 2ϕ2 transformation by applying elementary proofs. Then, by reversing the order of summation, we obtain eight multivariable extensions of transformations of terminating 2ϕ1 series. As limiting cases of our main results, we obtain three An1ϕ1 summation formulae.