tetration
Sign in to saveAlso known as hyper-4
thumb|alt=A colorful graphic with brightly colored loops that grow in intensity as the eye goes to the right|Domain coloring of the holomorphic tetration {}^{z}e, with [[hue representing the function argument and brightness representing magnitude]] thumb|alt=A line graph with curves that bend upward dramatically as the values on the x-axis get larger|{}^{n}x, for , showing convergence to the infinitely iterated exponential between the two dots
~32 min read
Encyclopedic overview
27 sectionsContents
- Introduction
- Terminology
- Notation
- Examples
- Extensions
- Extension of domain for bases
- Base zero
- Complex bases
- Extensions of the domain for different heights
- Infinite heights
- Negative heights
- Linear approximation for real heights
- Higher order approximations for real heights
- Complex heights
- Ordinal tetration
- Non-elementary recursiveness
- Inverse operations
- Super-root
- Square super-root
- Other super-roots
- Super-logarithm
- Open questions
- Applications
- See also
- References
- External links
- Further reading
thumb|alt=A colorful graphic with brightly colored loops that grow in intensity as the eye goes to the right|Domain coloring of the holomorphic tetration {}^{z}e, with [[hue representing the function argument and brightness representing magnitude]] thumb|alt=A line graph with curves that bend upward dramatically as the values on the x-axis get larger|{}^{n}x, for , showing convergence to the infinitely iterated exponential between the two dots
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no universal notation for tetration, though Knuth's up arrow notation \uparrow \uparrow and the left-exponent {}^{x}b are common.
Excerpted from Wikipedia’s “tetration” article, available under the CC BY-SA 4.0 licence.