Manuals/calci/TETRATE

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TETRATE(a,n)


  • is the base value.
  • is power value.

Description

  • This function shows the tetration value of the given number.
  • In , is the base value and is the power value.
  • The hyperoperation after exponentiation is Tetration.
  • Tetration is called iterated exponentiation.
  • The notation means Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double exponent: use braces to clarify"): {\displaystyle a^{a}^{\cdots }^{a}} the application of exponentiation times.
  • For any positive real a>0 and non-negative integer we define by:

Failed to parse (unknown function "\begin{cases}"): {\displaystyle ^n a = \begin{cases} 1, & \mbox{if }n\mbox{=0} \\ a^{[(n-1)a]}, & \mbox{if }n\mbox{ >0} \end{cases}}

f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}