H\"older and Kurokawa meet Borwein--Dykshoorn and Adamchik

TL;DR

This paper reveals connections between Kurokawa's multiple trigonometric functions and functions by Borwein-Dykshoorn and Adamchik, linking identities involving special constants like ζ(3), π, and G.

Contribution

It establishes new mathematical links between different special functions and identities involving fundamental constants, expanding understanding of their interrelations.

Findings

Identifies a link between Kurokawa functions and Borwein-Dykshoorn, Adamchik functions.

Shows how identities involving ζ(3), π, and G are interconnected.

Provides new proofs and relations among these special constants.

Abstract

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 $\zeta(3)$, $\pi$ and the Catalan constant $G$ that are proved in these three papers are related.