Manuals/calci/TETRATE

TETRATE(a,n)

• $a$ is the base value.
• $n$ is power value.

Description

• This function shows the tetration value of the given number.
• In $TETRATE(a,n)$,$a$ is the base value and $n$ is the power value.
• The hyperoperation after exponentiation is Tetration.
• Tetration is called iterated exponentiation.
• The notation $^{n}a$ 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 $n-1$ times.
• For any positive real a>0 and non-negative integer $n\geq 0$ we define $^{n}a$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

• SLOG
• SUPERLOGARITHM
• TETRA

References

• https://en.wikipedia.org/wiki/Tetration

• List of Main Z Functions
• Z3 home