Difference between revisions of "Manuals/calci/LOGSTAR"
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| − | LOGSTAR | + | <div style="font-size:30px">'''LOGSTAR (Number,Base)'''</div><br/> |
| + | *<math>Number</math> is any real number. | ||
| + | *<math>Base</math> base value of the log. | ||
| + | |||
| + | ==Description== | ||
| + | *This function shows the iterated logarithm of the given number. | ||
| + | *In <math>LOGSTAR (Number,Base)</math>, <math>Number</math> is any real number. | ||
| + | *<math>Base</math> is the base value of the log. | ||
| + | *Log star is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1. | ||
| + | *The simple definition of the Log star is : | ||
| + | <math>\begin{cases} | ||
| + | 0 & if n\le 1 \\ | ||
| + | 1+log*(log n) & ifn > 1 \\ | ||
| + | \end{cases} | ||
| + | *The relation between Log star and Super logarithm is log*n=[slog_e(n)] for positive real numbers. | ||
| + | *Also for negative real numbers ,log star value is 0,whereas | ||
Revision as of 15:07, 23 May 2017
LOGSTAR (Number,Base)
- 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 Number} is any real number.
- 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 Base} base value of the log.
Description
- This function shows the iterated logarithm 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 LOGSTAR (Number,Base)} , 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 Number} is any real number.
- 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 Base} is the base value of the log.
- Log star is the number of times the logarithm function must be iteratively applied before the result is less than or equal to 1.
- The simple definition of the Log star is :
<math>\begin{cases} 0 & if n\le 1 \\ 1+log*(log n) & ifn > 1 \\ \end{cases}
- The relation between Log star and Super logarithm is log*n=[slog_e(n)] for positive real numbers.
- Also for negative real numbers ,log star value is 0,whereas