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<p>In this paper, using the generating function of Wright functions we give new differential and series representations for the Wright functions. We also present some integral identities involving the Bourguet, Schläfli, Neumann, Poisson, Sonine and Sonine-Gegenbauer integrals as integral representations for the Wright functions and their products. We further study an addition formula for the Prabhakar function, and its relationship with the Wright function is discussed. Moreover, some improper integral involving the Wright functions are given using the inverse Laplace transforms of the exponential and Mittag-Leffler functions.</p>

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Some differential, series and integral representations for the wright functions

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Alireza Ansari,
  • Hassan Askari

摘要

In this paper, using the generating function of Wright functions we give new differential and series representations for the Wright functions. We also present some integral identities involving the Bourguet, Schläfli, Neumann, Poisson, Sonine and Sonine-Gegenbauer integrals as integral representations for the Wright functions and their products. We further study an addition formula for the Prabhakar function, and its relationship with the Wright function is discussed. Moreover, some improper integral involving the Wright functions are given using the inverse Laplace transforms of the exponential and Mittag-Leffler functions.