On Hermite–Padé approximants for the product of two logarithms

The Hermite–Padé approximants for systems of functions, containing $\ln (1 + 1 / z)\ln (1-1 / z)$ are considered. The research is motivated by the number-theoretic applications related to Diophantine approximations for products of logarithms. Two constructions are considered, for which it is possible to find an explicit form of Hermite–Padé approximants. Their asymptotic behavior is studied and convergence is proved.