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<p>Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial role. We also give an interesting application of our result, namely, a new summation formula for some derivatives of the Bessel functions of the first kind and the Struve functions with respect to the order.</p>

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A series of definite integrals involving upper incomplete Gamma functions

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Mátyás Barczy,
  • István Mező

摘要

Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial role. We also give an interesting application of our result, namely, a new summation formula for some derivatives of the Bessel functions of the first kind and the Struve functions with respect to the order.