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<p>In this sequel, using various techniques, we derive several formulas involving Gaussian hypergeometric functions, Appell hypergeometric function <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_978_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(F_1\)</EquationSource> </InlineEquation>, and Legendre functions from the connection between two bases of the representation space on a group of unimodular Diag (1, −&#xa0;1, −&#xa0;1) matrices.</p>

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On some series and index integrals involving 2\(F_1\) and a reduction formula for the appell function \(F_1\)

  • 期刊论文

  • 发表日期：

    2025年10月23日

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  • I. A. Shilin,
  • J. Choi

摘要

In this sequel, using various techniques, we derive several formulas involving Gaussian hypergeometric functions, Appell hypergeometric function \(F_1\) , and Legendre functions from the connection between two bases of the representation space on a group of unimodular Diag (1, − 1, − 1) matrices.