Difference between revisions of "Manuals/calci/TETRATE"
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*The hyperoperation after exponentiation is Tetration. | *The hyperoperation after exponentiation is Tetration. | ||
*Tetration is called iterated exponentiation. | *Tetration is called iterated exponentiation. | ||
| − | *The notation <math>^n a</math> means <math> a^a^ | + | *The notation <math>^n{a}</math> means <math> a^{a^{a}}</math> the application of exponentiation <math> n-1</math> times. |
| − | *For any positive real a>0 and non-negative integer <math>n\ge 0</math> we define <math>^n a</math>by: | + | *For any positive real a>0 and non-negative integer <math>n\ge 0</math> we define <math>^n{a}</math>by: |
| − | <math>^n a = | + | <math>^n{a} = |
\begin{cases} | \begin{cases} | ||
| − | 1, & \mbox{if }n\mbox{=0} \\ | + | 1, & \mbox{if }n\mbox{ =0} \\ |
| − | a^{ | + | a^{a^{(n-1)}}, & \mbox{if }n\mbox{ >0} \\ |
| − | \end{cases}</math> | + | \end{cases} |
| + | </math> | ||
==Examples== | ==Examples== | ||
| Line 31: | Line 32: | ||
==References== | ==References== | ||
| − | *https://en.wikipedia.org/wiki/Tetration | + | *[https://en.wikipedia.org/wiki/Tetration Tetration] |
*[[Z_API_Functions | List of Main Z Functions]] | *[[Z_API_Functions | List of Main Z Functions]] | ||
*[[ Z3 | Z3 home ]] | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 04:34, 27 May 2022
TETRATE(a,n)
- is the base value.
- is power value.
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 the application of exponentiation times.
- For any positive real a>0 and non-negative integer we define by:
,
means 
the application of exponentiation 
times.
we define 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} }
Examples
- TETRATE (3,2) = 27
- TETRATE (4,3) = 1.3407807929942597e+154
- TETRATE (10,2) = 10000000000
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See Also
References