On p-adic analytic continuation with applications to generating elements

Given a prime number p and the Galois orbit O(T) of an integral transcendental element T of Cp, the topological completion of the algebraic closure of the field of p-adic numbers, we study the p-adic analytic continuation around O(T) of functions defined by limits of sequences of restricted power series with p-adic integer coefficients. We also investigate applications to generating elements for Cp or for some classes of closed subfields of Cp.