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^a</math>.
+
*The notation <math>^n{a}</math>  means <math> a^{a^{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>a^{a}^cdots^{a}^</math>
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\begin{cases}
*<math>\overbrace{ 1+2+\cdots+100 }</math>
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1,  & \mbox{if }n\mbox{ =0} \\
*<math>\cdots</math>
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a^{a^{(n-1)}}, & \mbox{if }n\mbox{ >0} \\
 +
\end{cases}
 +
</math>
 +
 
 +
==Examples==
 +
#TETRATE (3,2) = 27
 +
#TETRATE (4,3) = 1.3407807929942597e+154
 +
#TETRATE (10,2) = 10000000000
 +
 
 +
==Related Videos==
 +
 
 +
{{#ev:youtube|v=kITJ6qH7jS0|280|center|Exponent}}
 +
 
 +
==See Also==
 +
*[[Manuals/calci/SLOG| SLOG]]
 +
*[[Manuals/calci/SUPERLOGARITHM| SUPERLOGARITHM]]
 +
*[[Manuals/calci/TETRA| TETRA]]
 +
 
 +
==References==
 +
*[https://en.wikipedia.org/wiki/Tetration Tetration]
 +
 
 +
 
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 04:34, 27 May 2022

TETRATE(a,n)


  • 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:

Failed to parse (unknown function "\begin{cases}"): {\displaystyle ^n{a} = \begin{cases} 1, & \mbox{if }n\mbox{ =0} \\ a^{a^{(n-1)}}, & \mbox{if }n\mbox{ >0} \\ \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

References