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>^n a = \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 13:14, 1 June 2017
TETRATE(a,n)
- 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 a} is the base value.
- 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} is power value.
Description
- This function shows the tetration value of the given number.
- In 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 TETRATE(a,n)} ,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 a} is the base value and 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} is the power value.
- The hyperoperation after exponentiation is Tetration.
- Tetration is called iterated exponentiation.
- The notation 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} means 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 a^a^\cdots^a} the application of exponentiation 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-1} times.
- For any positive real a>0 and non-negative integer 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\ge 0} 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} by:
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^{[(n-1)a]}, & \mbox{if }n\mbox{ >0} \end{cases}}