Mathematics

Presentations

• Lambert's W Function, Infinite Exponentials, Powertowers, Iterated Exponentials and Tetration
  1. The Author's Strange Encounter With Johann Heinrich Lambert
  2. Infinite Exponentials (often called infinitely iterated exponentials or exponential towers)
  3. A Slightly Deeper Analysis of Infinite Exponentials
  4. A MacLaurin Expansion for Lambert's W function
  5. Approximating the Principal Branch of the Complex Lambert's W Function
  6. Approximating the Branches of the Complex Lambert's W Function Using Analytic Continuation
  7. An Infinite Family of Hyper-Lambert Functions And Their Use In Solving Exponential Tower Equations
  8. A Detailed Look at the Hyperroot Functions Using Lambert's W Function
  9. A Continuous Extension of the hyper4 Operator
  10. An Infinitely Differentiable Extension for the hyper4 Operator
  11. A Series Expansion for ^m(e^x) Using Lambert's W Function
  12. A More Consistent Definition of Tetration for Rational Exponents
  13. The General Infinite Exponential and its Limit
  14. The Analytic Continuation of the Infinite Hyperpower Function F(x) = ^+∞x
  15. The Birth of the Infinite Tetration Fractal
  16. A Strange Hyperexponential Series
  17. Solving the First Auxiliary Real Exponential Equation using Lambert's W function
  18. Solving the Second Auxiliary Real Exponential Equation using Lambert's W function
  19. Solving the n-th Auxiliary Real Exponential Equation
  20. A Family of Hyperpower/Hyperfactorial Series
  21. File Signatures and Tetration of 2
  22. An Infinite Hierarchy of Hyperfactorial Functions
  23. A Collection of References for Infinite Exponentials and Tetration
• Various
  1. An Interesting Sequence of Cyclic Digits
  2. Suprema and Infima in Real Life
  3. The Cantor Function
  4. The 3n+1 problem
  5. Temperatures on The Surface of the Earth
  6. A Program to Solve Loyd's Wooden Tile Puzzle
  7. Is There a Limit on How Fast the Olympic 100 Meters Can Be Ran?
  8. Modelling Time Under Total Anesthesia
  9. The Author's View of the Universe
  10. The Author's Puzzles
  11. Distinct Resistances Possible With at Most n Distinct Resistors
  12. Can Mathematics Explain What Is Real?
  13. Estimating the Area and Perimeter of a Circle and π Using Archimedes' Method
  14. The Most Beautiful Construction in Mathematics
  15. Overall Function Behavior
  16. Does Arc Light Flickering Interfere With Video?
  17. Understanding Symbolic Levels
  18. Trends in Euler's Totient φ Function
  19. The Author's Webpage Statistics Projector
  20. Using Maple to Visualize the Complex w-Plane
  21. From Mathematics To Color Perception
  22. A Short Tutorial On Big Numbers
  23. Modelling Relative Mind Power Using the ELO Rating System
  24. Every Chess Configuration
  25. Should New Mathematics Ideas Be Announced?
  26. How Does tinyurl Work?
  27. The Main Principles of a Chess Engine
  28. The Dynamics of Computer Programming
  29. Is The Mind Infinite?
  30. An Almost Impossible Puzzle Designed For The Author by His Father

Function/data graphs were done with Maple and THINK Pascal and geometrical schematics with EucliDraw.

Papers

1. "On An Application Of Lambert's W Function to Infinite Exponentials", Complex Variables, 49(11) (Sep. 2004), 759-780.
2. "On Solving the p-th Complex Auxiliary Equation f^(p)(z)=z", Complex Variables, 50(13) (Oct. 2005), 977-997.
3. "Lambert's W Function and Convergence of Infinite Exponentials in the Space of Quaternions", Complex Variables, 51(12) (Dec. 2006), 1129-1152.
4. "Corrigendum for 3", Complex Variables, 52(4), (Apr. 2007), 351.
5. "Explicit Solution of the Kepler Equation" (with Alexandr Dubinov), Physics of Particles and Nuclei, Letters, 4(3) (May 2007), 213-216.
6. "On Some Applications of the Generalized Hyper-Lambert Functions", Complex Variables, 52(12) (Dec. 2007), 1101-1119.

1. "On The Convergence of Series With Infinite Exponentials and Iterated Factorials".
2. "On Extending hyper4 and Knuth's Up-arrow Notation to the Reals".
3. "On a Probabilistic Theorem for the Asymptotic Densities of φ, the Timing of the Euclidian GCD Algorithm and a Tetration Function".
4. "An Almost Everywhere Analytic Extension of Tetration" (work in progress).

• The author's math pages and papers are devoted to his parents and his superb mathematics teacher: Kostas Sourlas.

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