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<p>In this paper we consider some computational applications of the conjugate Appell-Simpson polynomial sequences, recently introduced. Particularly, the Umbral-Simpson interpolation is studied both in the continuous and discrete case. Two new classes of interpolatory quadrature rules, which include the classic 1/3 Simpson formula and the midpoint formula, are obtained. A new operator of Jakimovski and Leviatan type is derived for the approximation of real functions on the semi-infinite axes. Several numerical examples are given. The results of this paper appear to be new.</p>

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The parabolic mean operator and related polynomial sequences 2: applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • Francesco A. Costabile,
  • Maria Italia Gualtieri,
  • Anna Napoli

摘要

In this paper we consider some computational applications of the conjugate Appell-Simpson polynomial sequences, recently introduced. Particularly, the Umbral-Simpson interpolation is studied both in the continuous and discrete case. Two new classes of interpolatory quadrature rules, which include the classic 1/3 Simpson formula and the midpoint formula, are obtained. A new operator of Jakimovski and Leviatan type is derived for the approximation of real functions on the semi-infinite axes. Several numerical examples are given. The results of this paper appear to be new.