Difference between revisions of "Superlogarithm"
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[[Superlogarithm]] is quite ambiguous term. |
[[Superlogarithm]] is quite ambiguous term. |
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| − | [[Superlogarithm]] may refer to solution |
+ | [[Superlogarithm]] may refer to solution \(f\) of the [[transfer equation]] with transfer function [[logatirithm]], id est |
| − | + | \(f(z+1)=\ln(f(z))\) |
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The reasonable solution of this equation can be easily expressed through the [[natural tetration]] tet, |
The reasonable solution of this equation can be easily expressed through the [[natural tetration]] tet, |
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| − | + | \(f(z)=\mathrm{tet}(-z)\) |
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| − | Also, [[Superlogarithm]] may refer to the natural [[ArcTetration]] |
+ | Also, [[Superlogarithm]] may refer to the natural [[ArcTetration]] \(\mathrm{ate}=\mathrm{tet}^{-1}\), reminding that it is [[inverse function]] of [[SuperExponential]]. |
This analogy had been used choosing names [[fsexp.cin]] and [[fslog.cin]] for the [[C++]] numerical implementations of the [[natural tetration]] and the [[ArcTetration]]. |
This analogy had been used choosing names [[fsexp.cin]] and [[fslog.cin]] for the [[C++]] numerical implementations of the [[natural tetration]] and the [[ArcTetration]]. |
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Revision as of 18:49, 30 July 2019
Superlogarithm is quite ambiguous term.
Superlogarithm may refer to solution \(f\) of the transfer equation with transfer function logatirithm, id est
\(f(z+1)=\ln(f(z))\)
The reasonable solution of this equation can be easily expressed through the natural tetration tet,
\(f(z)=\mathrm{tet}(-z)\)
Also, Superlogarithm may refer to the natural ArcTetration \(\mathrm{ate}=\mathrm{tet}^{-1}\), reminding that it is inverse function of SuperExponential.
This analogy had been used choosing names fsexp.cin and fslog.cin for the C++ numerical implementations of the natural tetration and the ArcTetration.
The ambiguity makes term Superlogarithm unwanted; in future, it is better to avoid it at all in any of its meanings. In particular, as soon as the more advanced algorithms for the tetration and the ArcTetration will be implemented, it is better to call them simply tet and ate, in the similar way, as the names of routines for elementary functions coincide with the names of these functions.