Calculus III: Taylor Series

Fractional Calculus and the Taylor-riemann Series

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Tayl...

Flows and stochastic Taylor series in Itô calculus

On the Taylor functional calculus

We give a Martinelli-Vasilescu type formula for the Taylor functional calculus and a simple proof of its basic properties.

From Taylor Series to Taylor Models

An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way. Utilizing differential algebraic and functional analytic arguments on ...

Universal Taylor series

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