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Abstract <p> In this paper, new formulas are obtained for estimating the remainder term arising from the summation of the hypergeometric series <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3054_Article_IEq1.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_D^{(N,j)}\)</EquationSource> </InlineEquation>. Such formulas allow one to effectively estimate the remainder of the summation when calculating the value of the function <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3054_Article_IEq1.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_D^{(N,j)}\)</EquationSource> </InlineEquation> in the unit polydisk. The obtained formulas can be used for calculation of the analytic continuation of the Lauricella function. </p>

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Estimation of the Remainder Term of the Hypergeometric Series \(G_D^{(N,j)}\)

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • S. I. Bezrodnykh,
  • O. V. Dunin-Barkovskaya

摘要

Abstract

In this paper, new formulas are obtained for estimating the remainder term arising from the summation of the hypergeometric series \(G_D^{(N,j)}\) . Such formulas allow one to effectively estimate the remainder of the summation when calculating the value of the function \(G_D^{(N,j)}\) in the unit polydisk. The obtained formulas can be used for calculation of the analytic continuation of the Lauricella function.