Manuals/calci/TETRATE

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}}

Examples

  1. TETRATE (3,2) = 27
  2. TETRATE (4,3) = 1.3407807929942597e+154
  3. TETRATE (10,2) = 10000000000

See Also

References