The real field with convergent generalized power series

We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on [0,1][0,1] by a series ∑cnxαn\sum c_{n} x^{\alpha _{n}} with 0≤αn→∞0 \leq \alpha _{n} \rightarrow \infty and ∑|cn|rαn1r>1 is definable. This expansion is polynomially bounded.