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<p>Using a new representation of the harmonic zeta function (also known as the Apostol–Vu zeta function), we establish an interesting connection between the special values of this function and a certain type of complex logarithmic integrals previously introduced by Glasser and Manna which proved to be useful in the study of the Laplace transform of the digamma function. To our knowledge, this unexpected connection has not been noticed before.</p>

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New insights into Glasser–Manna integrals and the harmonic zeta function

  • 期刊论文

  • 发表日期：

    2025年6月22日

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  • Marc-Antoine Coppo,
  • Bernard Candelpergher

摘要

Using a new representation of the harmonic zeta function (also known as the Apostol–Vu zeta function), we establish an interesting connection between the special values of this function and a certain type of complex logarithmic integrals previously introduced by Glasser and Manna which proved to be useful in the study of the Laplace transform of the digamma function. To our knowledge, this unexpected connection has not been noticed before.