Difference between revisions of "Manuals/calci/TETRATE"
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*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> = | + | <math>^n a</math> = \begin{cases} |
| − | \begin{cases} | ||
1, & \mbox{if }n\mbox{=0} \\ | 1, & \mbox{if }n\mbox{=0} \\ | ||
a^{[(n-1)a]}, & \mbox{if }n\mbox{ >0} | a^{[(n-1)a]}, & \mbox{if }n\mbox{ >0} | ||
\end{cases}</math> | \end{cases}</math> | ||
Revision as of 14:14, 1 June 2017
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 = \begin{cases} 1, & \mbox{if }n\mbox{=0} \\ a^{[(n-1)a]}, & \mbox{if }n\mbox{ >0} \end{cases}</math>