We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara, Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with one generator. We apply these results to show that the full sets of shuffle relations of polylogarithms and regularized MZVs are derived by a single series. We also take this approach to study the extended double shuffle relations of MZVs by comparing these shuffle relations with the quasi-shuffle relations of the regularized MZVs in our previous approach of MZVs by renormalization.
Harmonic-Number Summation Identities, Symmetric Functions, and Multiple Zeta Values
A cyclic analogue of multiple zeta values
Iterated integrals on $\mathbb{P}^{1}\setminus\{0,1,\infty,z\}$ and a class of relations among multiple zeta values
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