  In this article, we set up a method of reconstructing to polylogarithms
$\mathrm{Li}_k(z)$ from zeta values $\zeta(k)$ via the Riemann-Hilbert problem.
This is referred to as "a recursive Riemann-Hilbert problem of additive type."
Moreover, we suggest a framework of interpreting the connection problem of the
Knizhnik-Zamolodochikov equation of one variable as a Riemann-Hilbert problem.
