Hyperoperation

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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:


  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}\,\!