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Abstract <p>Integral representations and estimates for the remainder terms of the Appell double hypergeometric series <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({{F}_{2}}\)</EquationSource> <!--ComMat2570150Bezrodnykh-m1--> </InlineEquation> are constructed. The found formulas can be used to develop algorithms for computing the Appell functions <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({{F}_{1}}\)</EquationSource> <!--ComMat2570150Bezrodnykh-m2--> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({{F}_{3}}\)</EquationSource> <!--ComMat2570150Bezrodnykh-m3--> </InlineEquation> in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({{\mathbb{C}}^{2}}\)</EquationSource> <!--ComMat2570150Bezrodnykh-m4--> </InlineEquation> by applying analytic continuation formulas. The results have applications to problems in mathematical physics and computational function theory, including the construction of conformal mappings of complex polygons based on the Schwarz–Christoffel integral.</p>

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Estimation of the Remainder Term of the Appell Hypergeometric Series F2

  • 期刊论文

  • 发表日期：

    2025年12月1日

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

摘要

Abstract

Integral representations and estimates for the remainder terms of the Appell double hypergeometric series \({{F}_{2}}\) are constructed. The found formulas can be used to develop algorithms for computing the Appell functions \({{F}_{1}}\) and \({{F}_{3}}\) in \({{\mathbb{C}}^{2}}\) by applying analytic continuation formulas. The results have applications to problems in mathematical physics and computational function theory, including the construction of conformal mappings of complex polygons based on the Schwarz–Christoffel integral.