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^\cdots^a</math> the application of exponentiation <math> n-1</math> times. | + | *The notation <math>^n{a}</math> means <math> a^{a}^\cdots^{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 = | ||
Revision as of 04:13, 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 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:
,
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.
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
- TETRATE (3,2) = 27
- TETRATE (4,3) = 1.3407807929942597e+154
- TETRATE (10,2) = 10000000000
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References