A reduction formula for length-two polylogarithms and some applications

Matilde N. Lalín, Jean-Sébastien Lechasseur
2018 Revista de la Unión Matemática Argentina  
We use shuffle and stuffle relations to give a simple proof of a reduction formula for length-two multiple polylogarithms evaluated in complex parameters of absolute value 1 in terms of a finite sum of products of lengthone polylogarithms. This result was originally due to Nakamura and recently reproved by Panzer by different methods. This generalises results of Borwein and Girgensohn for alternating Euler sums and for multiple zeta values twisted by fourth roots of unity by the first author.
more » ... the first author. We also explore implications for other colored multiple zeta values and present some applications to Mahler measure and Feynman diagrams.
doi:10.33044/revuma.v59n2a05 fatcat:ksvaj5pmbja2rjooedb274ufoy