| Abstract: | In this article we survey the basic results concerning the convergence of Infinite Exponentials; we use Lambert's W function to show convergence for the real and complex cases in a more elegant way and prove several incidental results about Infinite Exponentials. We also show how to extend analytically the Infinite Exponential function over the complex plane and how to derive exact expansions for finite and infinite power iterates of the hyperpower function. As a final application we derive several series identities involving Infinite Exponentials. |
