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<p>The Le Roy function and its extensions have gained noticeable interest within the context of diverse applications in calculus. We study an extension of the Le Roy function, its relevant properties, regarding e.g. integration and successive derivatives, through a formalism of operational nature. The results obtained in this note, in the light of Umbral Calculus, provide simplifying means for their use in the study of specific problems as in Physics and fractional order models.</p>

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On the properties of the Le Roy function and of its generalized forms

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Alessandro Curcio,
  • Giuseppe Dattoli,
  • Emanuele Di Palma

摘要

The Le Roy function and its extensions have gained noticeable interest within the context of diverse applications in calculus. We study an extension of the Le Roy function, its relevant properties, regarding e.g. integration and successive derivatives, through a formalism of operational nature. The results obtained in this note, in the light of Umbral Calculus, provide simplifying means for their use in the study of specific problems as in Physics and fractional order models.