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February 28, 2026Журнал вычислительной математики и математической физики / Computational Mathematics and Mathematical Physics0 citations

Estimation of the Remainder Term of the Appel Hypergeometric Series

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SBS.I. Bezrodnykh

Key Points

  • This research aims to construct integral representations and estimates for the remainder term of the Appell hypergeometric series.
  • Developed formulas for estimating the remainder term of the Appell hypergeometric series.
  • Examined applications in algorithm development using C programming with analytic continuation formulas.
  • Applied findings to mathematical physics and computational function theory.
  • Provided new integral representations for the remainder term of the Appell series.
  • Demonstrated practical applications in constructing conformal mappings for complex polygons.

Abstract

Integral representations and estimates for the remainder term for the summation of the double hypergeometric Appell series are constructed. The resulting formulas have applications in developing algorithms for computing the Appell functions and in C using analytic continuation formulas. The results have applications to problems in mathematical physics and computational function theory, including the construction of conformal mappings of complicated polygons based on the Christoffel-Schwarz integral.

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Cite This Study

S.I. Bezrodnykh (2025) studied this question.

synapsesocial.com/papers/69a287130a974eb0d3c02758https://doi.org/10.7868/s3034533225120015
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