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<p>The standard literature on special functions contains a lot of hypergeometric identities involving products and quotients of gamma functions, but still the occurrence of such identities is a sporadic phenomenon. This is because the existence of them is constrained by severe arithmetic conditions. We demonstrate this kind of constraints by focusing on a certain data region where the essential nature of the issue comes out clearly.</p>

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Arithmetic constraints on hypergeometric identities

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Katsunori Iwasaki,
  • Mina Kusakabe

摘要

The standard literature on special functions contains a lot of hypergeometric identities involving products and quotients of gamma functions, but still the occurrence of such identities is a sporadic phenomenon. This is because the existence of them is constrained by severe arithmetic conditions. We demonstrate this kind of constraints by focusing on a certain data region where the essential nature of the issue comes out clearly.