Difference between revisions of "Manuals/calci/TETRATE"

Revision as of 13:13, 1 June 2017

TETRATE(a,n)

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:

$^{n}a$ = \begin{cases} 1, & \mbox{if }n\mbox{=0} \\ a^{[(n-1)a]}, & \mbox{if }n\mbox{ >0} \end{cases}</math>

@@ Line 8: / Line 8: @@
 *The hyperoperation after exponentiation is Tetration.
 *Tetration is called iterated exponentiation.
-*The notation <math>^n a</math>  means <math> a^a^a</math>.
+*The notation <math>^n a</math>  means <math> a^a^\cdots^a</math> the application of exponentiation <math> n-1</math> times.
-* <math>a^{a}^{\dots}^{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:
-*Tetration is simply defined by:For any positive real  a>0 and non-negative integer  we define by:
+<math>^n a</math> =
-<math>a^{a}^cdots^{a}^</math>
+\begin{cases}
-*<math>\overbrace{ 1+2+\cdots+100 }</math>
+,  & \mbox{if }n\mbox{=0} \\
-*<math>a^2</math>
+a^{[(n-1)a]}, & \mbox{if }n\mbox{ >0}
+\end{cases}</math>