New 3 and 6-Term Functional Dilogarithm Equations from Beta-Type Integrals

Abstract

Building on results by Abouzahra and Lewin, McIntosh, and Kirilov we derive new functional dilogarithm equations and consequent diologarithim ladders. By showing that the ratio of a pair of sextic and cubic integrals equals a rational constant, we construct new 3- and 6-term functional equations, from which we derive an analytic proof of an identity by Loxton-Lewin, as well as a pair of quartic-base dilogarithm ladders, also believed to be new, building on Loxton's result. Finally, we prove conjectured 2-term dilogarithm identities of Bytsko, and extend his result for the Bloch-Wigner function using the above methods.