Tetration FAQ Discussion

[andydude]

The more I think about it, the more I think that the FAQ and the formula sheet should be combined.

Here is a combined outline for the possible merge of the two:

• Preamble
  
  
• Introduction to Hyper-operators
  
  • What is the Ackermann function?
    
  • Hyper-operator notation
    
  • Hyper-operator terminology
    
  • Hyper-operator identities
    
  
  
• Introduction to Tetration
  
  • Tetration as the hyper-4-operator
    
  • Tetration notation and terminology
    
  • Sequence of n-th tetrates
    
  • Standard extensions of tetration
    
    • Extending tetration to zero base
      
    • Extending tetration to complex bases
      
    • Extending tetration to negative heights
      
    • Extending tetration to infinite heights
      
  
  
• Introduction to Iteration
  
  • Dynamical systems translation equation
    
  • Abel's functional equation
    
  • Schroeder's functional equation
    
  • Boettcher's functional equation
    
  • Julia's functional equation
    
  • Tetration vs. Iterated Exp
    
  
  
• Exponentiation and factorials
  
  • Table of exponentiation
    
  • Extension of exponentiation
    
  • Extension of factorials
    
  • Extension of super-factorials
    
  
  
• Topological conjugacy
  
  • Lambert-W-like conjugates (srt2(x), W(x), x^^oo)
    
  • Exponential-like conjugates (b^x = (h^(1/h))^x, h^x - 1)
    
  • Topological conjugacy of the super-logarithm
    
  
  
• Other extensions of Tetration
  
  • Ingolf Dahl's solution
    
  • Ioannis Galidakis' solution
    
  • Daniel Geisler's solution
    
  • Gottfried Helms' solution
    
  • Robert Munafo's solution
    
  • Cliff Nelson's solution
    
  • Peter Walker's solution
    
    • Andrew Robbins' solution
      
    • Jay D. Fox's solution
      
  
  
• Other extensions of Hyper-operators
  
  • Bromer's mixed hyper-operators
    
  • Munafo's lower hyper-operators
    
  • Trappmann's binary-tree hyper-operators
    
  • Trappmann's associative/commutative hyper-operators
    
  • Trappmann's balanced hyper-operators
    

@Henryk
If you could provide the TeX source for your FAQ, I will combine it with the formula sheet...

Andrew Robbins