On some constants related to the harmonic zeta function - Université Côte d'Azur
Preprints, Working Papers, ... Year : 2024

On some constants related to the harmonic zeta function

Bernard Candelpergher
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Abstract

We study a wide range of constants which are closely related to the harmonic zeta function ζ_H. Furthermore, by means of a new representation of ζ_H, we derive a new integral representation for ζ(n), as well as new evaluations for a variety of integrals of the same type as those previously considered by Glasser and Manna in connection with the Laplace transform of the digamma function.
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Dates and versions

hal-03602568 , version 1 (09-03-2022)
hal-03602568 , version 2 (19-05-2024)
hal-03602568 , version 3 (28-05-2024)
hal-03602568 , version 4 (01-10-2024)
hal-03602568 , version 5 (08-10-2024)

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  • HAL Id : hal-03602568 , version 5

Cite

Marc-Antoine Coppo, Bernard Candelpergher. On some constants related to the harmonic zeta function. 2024. ⟨hal-03602568v5⟩
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