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<p>In this paper, we derive the inverse Laplace transforms of several selected functions and present their explicit analytic representations in terms of confluent and generalized hypergeometric functions. These results are then applied to obtain several new summations formulas for alternating series involving gamma, digamma and trigamma functions. Several special cases and corollaries are presented to illustrate the usefulness of the method.</p>

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On the inverse Laplace transforms of selected functions and their applications

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Khaled Mehrez,
  • Abdulaziz Alenazi

摘要

In this paper, we derive the inverse Laplace transforms of several selected functions and present their explicit analytic representations in terms of confluent and generalized hypergeometric functions. These results are then applied to obtain several new summations formulas for alternating series involving gamma, digamma and trigamma functions. Several special cases and corollaries are presented to illustrate the usefulness of the method.