# Difference between revisions of "File:Expc.jpg"

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+ | The [[exponential]] iterated <math>c </math> times: |
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− | Importing image file |
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+ | <math>y=\exp^c(x)</math> versus <math>x</math> for some real values of <math>c</math> |
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+ | <br> |
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+ | The representation through the [[tetrational]] is used:<br> |
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+ | <math>\exp^c(z)=\mathrm{tet}\Big(c+\mathrm{tet}^{-1}(z)\Big)</math> |
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+ | |||

+ | This picture was stored at CZ |
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+ | |||

+ | The quick implementation from the [[Vladikavkaz Mathematical Journal]] |
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+ | <ref name="vladi"> |
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+ | http://www.ils.uec.ac.jp/~dima/PAPERS/2010vladie.pdf |
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+ | D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45. |
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+ | </ref> is used for the evaluation. |
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+ | |||

+ | [[File:ExpIte4T.jpg|200px|right]] |
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+ | http://en.citizendium.org/wiki/File:Expc.jpg |
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+ | and then also at wikipedia. |
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+ | |||

+ | Copyleft 2008 by Dmitrii Kouznetsov. Use for free, attribute the source. |
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+ | |||

+ | |||

+ | More detailed version of this figure, together with generators, is available, click the figure at right/ |
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+ | |||

+ | ==References== |
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+ | <references/> |
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+ | |||

+ | [[Category:Mathematical functions]] |
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+ | [[Category:Tetration]] |
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+ | [[Category:Superfunctions]] |
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+ | [[Category:Iteration]] |

## Latest revision as of 18:39, 11 July 2013

The exponential iterated \(c \) times\[y=\exp^c(x)\] versus \(x\) for some real values of \(c\)

The representation through the tetrational is used:

\(\exp^c(z)=\mathrm{tet}\Big(c+\mathrm{tet}^{-1}(z)\Big)\)

This picture was stored at CZ

The quick implementation from the Vladikavkaz Mathematical Journal
^{[1]} is used for the evaluation.

http://en.citizendium.org/wiki/File:Expc.jpg and then also at wikipedia.

Copyleft 2008 by Dmitrii Kouznetsov. Use for free, attribute the source.

More detailed version of this figure, together with generators, is available, click the figure at right/

## References

- ↑ http://www.ils.uec.ac.jp/~dima/PAPERS/2010vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.

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