Blossoming and Hermite-Padé approximation for hypergeometric series

Based on the blossoming theory, in this work we develop a new method for deriving Hermite-Padé approximants of certain hypergeometric series. Its general principle consists in building identities generalising the Hermite identity for exponentials, and in then applying their blossomed versions to appropriate tuples to simultaneously produce explicit expressions of the approximants and explicit integral representations of the corresponding remainders. For binomial series we use classical blossoms while for q-hypergeometric series we have to use q-blossoms.