__Presentations__^{[1]}

.__Lambert's W Function, Infinite Exponentials, Powertowers, Iterated Exponentials and Tetration__

(These are preliminary results, 10 years ago. For published versions of the majority of this section, consult the author's Google Scholar profile).- The Author's Strange Encounter With Johann Heinrich Lambert.
- Infinite Exponentials (often called infinitely iterated exponentials or exponential towers).
- A Slightly Deeper Analysis of Infinite Exponentials.
- A Maclaurin Expansion For Lambert's W function.
- Approximating the Principal Branch of the Complex Lambert's W Function.
- Approximating the Branches of the Complex Lambert's W Function Using Analytic Continuation.
- An Infinite Family of Hyper-Lambert Functions and Their Use In Solving Exponential Tower Equations.
- A Detailed Look at the Hyperroot Functions Using Lambert's W Function.
- A Continuous Extension of the hyper4 Operator.
- An Infinitely Differentiable Extension of the hyper4 Operator.
- A Series Expansion of
^{m}(e^{x}) Using Lambert's W Function. - A More Consistent Definition of Tetration For Rational Exponents.
- The General Infinite Exponential and Its Limit.
- The Analytic Continuation of the Infinite Hyperpower Function F(x) =
^{+∞}x. - The Infinite Tetration Fractal.
- The Exponential Fractal.
- A Strange Hyperexponential Series.
- Solving the First Auxiliary Real Exponential Equation Using Lambert's W Function.
- Solving the Second Auxiliary Real Exponential Equation Using Lambert's W Function.
- Solving the n-th Auxiliary Real Exponential Equation.
- A Family of Hyperpower/Hyperfactorial Series.
- File Signatures and Tetration of 2.
- A Collection of References For Infinite Exponentials and Tetration.
__Number Theory____Group Theory____Harmonic Analysis, Fourier Analysis, Spectral Theory____Analysis__- Suprema and Infima In Real Life.
- The Cantor Function.
- Temperatures On the Surface of the Earth.
- Is There a Limit On How Fast the Olympic 100 Meters Can Be Ran?
- Modelling Time Under Total Anesthesia.
- An Infinite Hierarchy of Hyperfactorial Functions.
- Overall Function Behavior.
- Modelling Relative Mind Power Using the ELO Rating System.

__Combinatorics____Topology____Philosophy of Mathematics____Set Theory____Analytic Geometry____Financial Mathematics____Complex Analysis, Dynamical Systems and Fractals____The Mathematics of Chess____Computer Science and Cryptography____Numerical Analysis____Miscellaneous__

__Theses__^{[2]}

- "The Problem of the Crack in the 'Generally' Anisotropic Disk" (English Translation of the author's father's Ph.D. Thesis. Original Greek Title: "Το Πρόβλημα της Ρωγμής εις τον «Γενικώς» Ανισότροπον Δίσκον").
- "The Problem of the Infinite Exponential", thesis submitted to the Mathematics Department of the Agricultural University of Athens. English, Greek.
- Companion Maple code for some of the various exponential fractals of the thesis above, at: Maple Primes.

- Function/data graphs done with Maple and THINK Pascal and geometrical schematics with EucliDraw.
- Written in LaTeX.

__Citations__

- Google Scholar.
- For more publications and pre-prints, Research Gate.
- math.stackexchange.com.
- Links