The Hermite-Pade 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 of the values of certain G-functions. Two constructions are considered, for which it is possible to find an explicit form of Hermite-Pade approximants. Their asymptotic behavior is studied and convergence is proved.

multiple orthogonal polynomials, vector equilibrium problem, irrationality measure

Mathematical problems and theory of numerical methods

Lysov Vladimir Genrikhovich,  ,  KIAM RAS