This site is about tetration.
Tetration is an obscure mathematical operation that
currently falls under the category of *Pure Mathematics*,
because it has few applications.
Even so, many mathematicians
have been interested in tetration, because of the historical significance
of its relatives in the hyper-operator sequence,
and because it is easy to make very large numbers with tetration.

There are many related functions that are not exactly
tetration but are inter-connected in some way.
When someone thinks about *sine* or *cosine*,
they generally aren't the only things that come to mind. Usually
other related functions such as *tangent* or the rest of
the trigonometric functions also come to mind, or perhaps a
vague memory that they have something to do with triangles.

One function that is intimately related to tetration, that
is much more well-known than tetration,
is the Lambert W-function. This function allows
many differential equations and equations involving
exponentials to be solved in closed-form rather than having
to resort to numerical analysis only.
The Lambert W-function
is so well known that both *Maple* (`LambertW`

) and
*Mathematica* (`LambertW`

)
provide it as a built-in function.

Tetration and its associated functions have been studied for hundreds of years, so it has quite a history behind it. Most of its history has been the investigation of the infinite tetrate. This function, along with the square super-root, are isomorphic to the Lambert W-function, so any equation that one can solve can be solved by any of them.

This website is an attempt to bring together those things
that are related to tetration, or could possibly be of use
in understanding more about tetration, namely various
methods that have been used to
generalize iteration
to *continuous iteration*,
*fractional iteration*, *real-analytic iteration*, or
*complex-analytic iteration* (which could also be called
holomorphic iteration).

Pages listed hierarchicaly by section:

- Home
- About Me, the author of this site.
- Applications of integer tetration, infinite tetration, and the Lambert W-function.
- Identities, a collection of every equation for tetration I know about.
- Papers which I have written discussing new methods.
- Gallery, several graphs of tetration and related functions.
- Glossary of terms used on this website.
- References
- Hyperops (under construction)
- Functions (under construction)
- Self-power function
- Self-root function
- Iteration (under construction)
- Methods of iteration
- Tetration, which includes tables of values.
- Tetrates about tetration with a constant height and variable base.
- Tetrationals about tetration with a constant base and variable height.
- Super-roots about the inverse function of tetrate functions.
- Super-logarithms about the inverse function of tetrationals.
- Methods of tetration
- Towers