Difference between revisions of "File:Acosq1plotT.png"
(Importing image file) |
|||
| Line 1: | Line 1: | ||
| + | Graphic of real and imaginary parts of [[acosc1]]$\left( \mathrm e ^{ \mathrm i \pi/4 } x \right)$ versus $x$. |
||
| − | Importing image file |
||
| + | |||
| + | Define |
||
| + | $\mathrm{acosq}_1(z)=\mathrm{acosc}_1\left( \mathrm e ^{ \mathrm i \pi/4 } z \right)$ |
||
| + | |||
| + | Then |
||
| + | $\Re(\mathrm{acosq}_1(x))$ and $\Im(\mathrm{acosq}_1(x))$ are plotted versus $x$ with thick blue and thick red lines. |
||
| + | |||
| + | The thin lines show the real and imaginary parts the cubic polynomial corresponding to the truncation of the [[Taylor expansion]] at zero; |
||
| + | :\mathrm{expan}_1(z)=\frac{3 \pi}{2} |
||
| + | \frac{3 \pi z}{2}+\frac{3 \pi |
||
| + | z^2}{2}+\frac{3}{16} \pi \left(8+3 \pi |
||
| + | ^2\right) z^3+O\left(z^4\right)$ |
||
| + | :\mathrm{expanq}_1(z)=:\mathrm{expan}_1(z \mathrm e^{\rm i \pi /4})$ |
||
| + | |||
| + | [[Category:ArcCosc]] |
||
| + | [[Category:Explicit plot]] |
||
| + | [[Category:Taylor expansion]] |
||
Latest revision as of 09:41, 21 June 2013
Graphic of real and imaginary parts of acosc1$\left( \mathrm e ^{ \mathrm i \pi/4 } x \right)$ versus $x$.
Define $\mathrm{acosq}_1(z)=\mathrm{acosc}_1\left( \mathrm e ^{ \mathrm i \pi/4 } z \right)$
Then $\Re(\mathrm{acosq}_1(x))$ and $\Im(\mathrm{acosq}_1(x))$ are plotted versus $x$ with thick blue and thick red lines.
The thin lines show the real and imaginary parts the cubic polynomial corresponding to the truncation of the Taylor expansion at zero;
- \mathrm{expan}_1(z)=\frac{3 \pi}{2}
\frac{3 \pi z}{2}+\frac{3 \pi
z^2}{2}+\frac{3}{16} \pi \left(8+3 \pi
^2\right) z^3+O\left(z^4\right)$
- \mathrm{expanq}_1(z)=:\mathrm{expan}_1(z \mathrm e^{\rm i \pi /4})$
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:50, 20 June 2013 |  | 2,512 × 3,504 (379 KB) | Maintenance script (talk | contribs) | Importing image file |
- You cannot overwrite this file.
File usage
The following page links to this file:
