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Journal of the Ramanujan Mathematical Society

Volume 38, Issue 3, September 2023  pp. 265–273.

Hölder and Kurokawa meet Borwein–Dykshoorn and Adamchik

Authors:  J.-P. Allouche
Author institution: CNRS, IMJ-PRG, Sorbonne, 4 Place Jussieu, F-75252 Paris Cedex 05, France.

Summary:  Following our discovery of a nice identity in a recent preprint of Hu and Kim, we show a link between the Kurokawa multiple trigonometric functions and two functions introduced respectively by Borwein-Dykshoorn and by Adamchik. In particular several identities involving ζ(3), π and the Catalan constant G that are proved in these three papers are related.

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