A method for finding the optimal control of linear distributed-parameter systems using polynomial series is discussed. It is known that any polynomial series basis vector can be transformed into a Taylor polynomial by the use of a suitable transformation. In this paper, the optimal control of a distributed-parameter system is simplified into the solution of a linear two-point boundary value problem, and, as a result, the optimal control is obtained via a Taylor series. It is shown that the implementation of Taylor series for this problem involves the use of an ill-conditioned matrix commonly known as the Hilbert matrix. The optimal control of linear distributed-parameter systems using other polynomial series is then calculated by transforming the properties of the Taylor series into other polynomial series. The formulation is straightforward and convenient for digital computation. An illustrative example is given.