  We study algebraic independence problem for the Taylor coefficients of the
Anderson-Thakur series arisen as deformation series of positive characteristic
multiple zeta values (abbreviated as MZV's). These Taylor coefficients are
simply specialization of hyperderivatives of the Anderson-Thakur series. We
consider the prolongation of t-motives associated with MZV's, and then
determine the dimension of the t-motivic Galois groups in question under
certain hypothesis. By using Papanikolas' theory, it enables us to obtain the
desired algebraic independence result.
