Difference between revisions of "Manuals/calci/TETRATE"
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*The notation <math>^n a</math> means <math>a^{a}^{\dots}^{a}^</math> the application of exponentiation <math> n-1</math> times. | *The notation <math>^n a</math> means <math>a^{a}^{\dots}^{a}^</math> the application of exponentiation <math> n-1</math> times. | ||
*Tetration is simply defined by:For any positive real a>0 and non-negative integer we define by: | *Tetration is simply defined by:For any positive real a>0 and non-negative integer we define by: | ||
| − | <math>a^{a}^{\ | + | <math>a^{a}^{\cdots}^{a}^</math> |
Revision as of 12:50, 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}^{\dots}^{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.
- Tetration is simply defined by:For any positive real a>0 and non-negative integer we define 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 a^{a}^{\cdots}^{a}^}