Difference between revisions of "File:Arctra3tesT.jpg"

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)$

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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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+Agreement of the primary approximation of function [[ArcTra]] with
-Importing image file
+$\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)$
+<poem>
+$P_0(L)=-1$
+$P_1(L)=1-L/2$
+$P_2(L)=-1+3 L/2 -L^2/3$
+$P_3(L)=1-3L+11L^2/6-L^3/4$
+$P_4(L)=-1+5L-35L^2/6+25L^3/12-L^4/5$
+</poem>
+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==
+<poem><nomathjax><nowiki>
+</nowiki><nomathjax></poem>
+==[[Latex]] generator of labels==
+<poem><nomathjax><nowiki>
+</nowiki><nomathjax></poem>
+[[Category:ArcTra]]
+[[Category:Inverse function]]
+[[Category:Agreement map]]
+[[Category:C++]]
+[[Cateogry:Latex]]
+[[Category:Trappmann function]]