2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221218We propose hypergeometric constructions of simultaneous approximations to polylogarithms. These approximations suit for computing the values of polylogarithms and satisfy 4-term Apery-like (polynomial) recursions.11 pages, minor correctionsClassical Analysis and ODEsNumber Theory33C20, 33F10, 11J70, 11M06Approximations to -, di- and tri- logarithmstext