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(Complex map of the $-1$st iteration of exponent, which is also $1$th iteration of logarithm; $u+\mathrm i v= \exp^{-1}(x+\mathrm i y)=\ln(x+\mathrm i y)= \mathrm{tet}(-1+\mathrm{ate}(x+\mathrm i y))$ For the evaluation, the iterate of expon...)
 
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Revision as of 11:23, 28 July 2013

Complex map of the $-1$st iteration of exponent, which is also $1$th iteration of logarithm;

$u+\mathrm i v= \exp^{-1}(x+\mathrm i y)=\ln(x+\mathrm i y)= \mathrm{tet}(-1+\mathrm{ate}(x+\mathrm i y))$

For the evaluation, the iterate of exponential is expressed through tetration tet and arctetration ate. The complex double implementations FSEXP and FSLOG are used in the C++ code below.

C++ generator of curves

// Files ado.cin, conto.cin, fsexp.cin and fslog.cin should be loaded in the working directory in order to compile the code below.


Latex generator of labels

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current12:47, 28 July 2013Thumbnail for version as of 12:47, 28 July 20132,281 × 1,179 (544 KB)T (talk | contribs)resolution?
11:23, 28 July 2013Thumbnail for version as of 11:23, 28 July 20131,711 × 885 (370 KB)T (talk | contribs)shift for 2 pixels to the left
11:14, 28 July 2013Thumbnail for version as of 11:14, 28 July 20132,281 × 1,179 (541 KB)T (talk | contribs)Complex map of the $-1$st iteration of exponent, which is also $1$th iteration of logarithm; $u+\mathrm i v= \exp^{-1}(x+\mathrm i y)=\ln(x+\mathrm i y)= \mathrm{tet}(-1+\mathrm{ate}(x+\mathrm i y))$ For the evaluation, the iterate of expon...

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