Corecursive Coding of High Computational Derivatives and Power Series

We discuss the functional lazy techniques in generation and handling of arbitrarily long sequences of derivatives of numerical expressions in one variable''; the domain to which the paper belongs is usually nicknamed Automatic differentiation’‘. Two models thereof are considered, the chains of ``pure’’ derivatives, and the infinite power series, similar, but algorithmically a bit different. We deal with their arithmetic/algebra, and with more convoluted procedures, such as composition and reversion. Some more specific applications of these structures are also presented.