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arXiv · 2410.01456

Moments of the cot function, central factorial numbers and their links with the Dirichlet eta function at odd integers

Serge Iovleff
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Abstract

We investigate the properties of the moments of the cot function using the central factorial numbers. Using a new integral representation of the central factorial numbers, we find a new way to express these moments in terms of recursive sums and integrals. This allows us to compute 'recursive' generalized harmonic series and multiple integrals as a linear combination of the Dirichlet eta functions at odd integers.

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Serge Iovleff. 2024-10-02. Moments of the cot function, central factorial numbers and their links with the Dirichlet eta function at odd integers. https://arxiv.org/abs/2410.01456

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