Difference between revisions of "File:Arctra3tesT.jpg"
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| + | Agreement of the primary approximation of function [[ArcTra]] with |
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| − | Importing image file |
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| + | |||
| + | $\mathrm{ArcTra}(z)\approx $ $\mathrm{app3}(z)=$ $ \displaystyle |
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| + | \ln(z) \left(1+ \frac{1}{z} \sum_{m=0}^M \frac{P_m(\ln(z))}{z^m}\right)$ |
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| + | <poem> |
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| + | $P_0(L)=-1$ |
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| + | $P_1(L)=1-L/2$ |
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| + | $P_2(L)=-1+3 L/2 -L^2/3$ |
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| + | $P_3(L)=1-3L+11L^2/6-L^3/4$ |
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| + | $P_4(L)=-1+5L-35L^2/6+25L^3/12-L^4/5$ |
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| + | </poem> |
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| + | |||
| + | For $M\!=\!4$, the agreement $A=A_3(x+\mathrm i y) $ is shown; |
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| + | |||
| + | $\displaystyle |
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| + | \mathcal A_3(z)= $ $\displaystyle |
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| + | -\lg \left( |
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| + | \frac{ |\mathrm{tra}(\mathrm{app3}(z))-z| } |
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| + | { |\mathrm{tra}(\mathrm{app3}(z))| + |z|} |
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| + | \right)$ |
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| + | |||
| + | ==[[C++]] generator of curves== |
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| + | |||
| + | <poem><nomathjax><nowiki> |
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| + | </nowiki><nomathjax></poem> |
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| + | ==[[Latex]] generator of labels== |
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| + | |||
| + | <poem><nomathjax><nowiki> |
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| + | </nowiki><nomathjax></poem> |
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| + | |||
| + | [[Category:ArcTra]] |
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| + | [[Category:Inverse function]] |
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| + | [[Category:Agreement map]] |
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| + | [[Category:C++]] |
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| + | [[Cateogry:Latex]] |
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| + | [[Category:Trappmann function]] |
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Latest revision as of 08:30, 1 December 2018
Agreement of the primary approximation of function ArcTra with
$\mathrm{ArcTra}(z)\approx $ $\mathrm{app3}(z)=$ $ \displaystyle \ln(z) \left(1+ \frac{1}{z} \sum_{m=0}^M \frac{P_m(\ln(z))}{z^m}\right)$
$P_0(L)=-1$
$P_1(L)=1-L/2$
$P_2(L)=-1+3 L/2 -L^2/3$
$P_3(L)=1-3L+11L^2/6-L^3/4$
$P_4(L)=-1+5L-35L^2/6+25L^3/12-L^4/5$
For $M\!=\!4$, the agreement $A=A_3(x+\mathrm i y) $ is shown;
$\displaystyle \mathcal A_3(z)= $ $\displaystyle -\lg \left( \frac{ |\mathrm{tra}(\mathrm{app3}(z))-z| }
{ |\mathrm{tra}(\mathrm{app3}(z))| + |z|}
\right)$
C++ generator of curves
<nomathjax>
<nomathjax>
Latex generator of labels
<nomathjax>
<nomathjax>
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:10, 1 December 2018 |  | 2,575 × 2,558 (538 KB) | Maintenance script (talk | contribs) | Importing image file |
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