Log-sine evaluations of Mahler measures

Log-sine evaluations of Mahler measures
Jonathan M. Borwein, Armin Straub — Journal of the Australian Mathematical Society — Special issue dedicated to Alf van der Poorten — Volume 92, Number 1, 2012, Pages 15-36


We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of multiple Mahler measures.


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    author = {Jonathan M. Borwein and Armin Straub},
    title = {Log-sine evaluations of {M}ahler measures},
    journal = {Journal of the Australian Mathematical Society},
    year = {2012},
    volume = {92},
    number = {1},
    pages = {15--36},
    doi = {10.1017/S1446788712000067},