Difference between revisions of "Manuals/calci/TETRATE"
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\begin{cases} | \begin{cases} | ||
1, & \mbox{if }n\mbox{ =0} \\ | 1, & \mbox{if }n\mbox{ =0} \\ | ||
| − | a^{a^{(n-1)}}, & \mbox{if }n\mbox{ >0} | + | a^{a^{(n-1)}}, & \mbox{if }n\mbox{ >0} \\ |
| − | \ | + | \end{cases} |
| − | + | </math> | |
| − | |||
| − | \ | ||
| − | |||
| − | \end{cases}</math> | ||
==Examples== | ==Examples== | ||
Latest revision as of 04:34, 27 May 2022
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^{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^{a^{(n-1)}}, & \mbox{if }n\mbox{ >0} \\ \end{cases} }
Examples
- TETRATE (3,2) = 27
- TETRATE (4,3) = 1.3407807929942597e+154
- TETRATE (10,2) = 10000000000
Related Videos
See Also
References