Hyperoperation

A hyperoperation is a generalization of addition, multiplication, exponentiation, tetration, etc. They are often written using Knuth's up-arrow notation. Natural number level hyperoperations can be defined recursively as a piecewise function:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/simple.wikipedia.org/v1/":): {\displaystyle H_n(a, b) = \begin{cases} b + 1 & \text{if } n = 0 \\ a & \text{if } n = 1, b = 0 \\ 0 & \text{if } n = 2, b = 0 \\ 1 & \text{if } n \ge 3, b = 0 \\ H_{n-1}(a, H_n(a, b - 1)) & \text{otherwise} \end{cases}\,\! }