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arXiv · 2412.19866

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals

Glenn Bruda
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Abstract

Defining a family of recurrences, we generalize Comtet's formula for the generating function of the enumeration of indecomposable permutations. Consequently, we generalize Panaitopol's asymptotic expansion for the prime counting function, obtaining asymptotic expansions salient to the first Hardy-Littlewood conjecture.

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Glenn Bruda. 2024-12-27. Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals. https://arxiv.org/abs/2412.19866

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