On certain Mahler functions (Q2341941)

The authors consider a class of functions which are holomorphic in the unit disc and which satisfy a Mahler-type functional equation (first introduced by \textit{F. Pellarin} [``An introduction to Mahler's method for transcendence and algebraic independence'', preprint, \url{arxiv:1005.1216}). They prove hyper transcendence and algebraic independence for certain families of such functions. Furthermore, relations for transcendence degrees are shown. The proofs depend on Mahler's method.