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 $a^{a^{a}}$ 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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ^n{a} = \begin{cases} 1, & \mbox{if }n\mbox{ =0} \\ a^{a^{(n-1)}}, & \mbox{if }n\mbox{ >0} \end{cases}}

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

Examples

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

Related Videos

Exponent

See Also

• SLOG
• SUPERLOGARITHM
• TETRA

References

• Tetration

• List of Main Z Functions
• Z3 home