Polynomial and series solutions of dynamic equations on time scales

Much work paralleling the standard theory of linear differential equations has been done recently for dynamic equations on time scales, providing a unified treatment of the continuous and discrete analysis in this area. One area which is less developed is the theory of series solutions, partly due to the lack of sufficient differentiability in a general time scale, and also due to the lack of I an analogue for polynomials which enjoys all the properties of the polynomials over the real numbers. In this paper, we obtain results for series and polynomial solutions for certain classes of dynamic equations and/or certain time scales.