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<p>We give a Jackson integral representation for Kajihara’s <i>q</i>-hypergeometric series <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(W^{M,2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>W</mi> <mrow> <mi>M</mi> <mo>,</mo> <mn>2</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>. We construct a <i>q</i>-difference system that corresponds to this integral. This system is an extension of a variant of the <i>q</i>-hypergeometric equation of degree three, defined by Hatano–Matsunawa–Sato–Takemura. We show that this system includes the <i>q</i>-Appell–Lauricella system as a degeneration.</p>

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A Jackson integral representation for a multiple q-hypergeometric series and an extension of the q-Riemann–Papperitz system

  • 期刊论文

  • 发表日期：

    2025年12月9日

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  • Takahiko Nobukawa

摘要

We give a Jackson integral representation for Kajihara’s q-hypergeometric series \(W^{M,2}\) W M , 2 . We construct a q-difference system that corresponds to this integral. This system is an extension of a variant of the q-hypergeometric equation of degree three, defined by Hatano–Matsunawa–Sato–Takemura. We show that this system includes the q-Appell–Lauricella system as a degeneration.