File:Foias 5e-2.pdf
Jump to navigation
Jump to search
Size of this JPG preview of this PDF file: 800 × 471 pixels. Other resolutions: 320 × 188 pixels | 640 × 377 pixels | 1,024 × 603 pixels | 1,280 × 753 pixels | 3,475 × 2,045 pixels.
Original file (3,475 × 2,045 pixels, file size: 11 KB, MIME type: application/pdf)
Captions
Captions
Add a one-line explanation of what this file represents
Summary[edit]
| Description |
English: Evolution of the sequence for several values of . All of them lead to two accumulation points, viz. 1 and . The sequence is related to the en:Foias constant . |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:Foias 5e-2.pdf * File:Foias 5e-2 svg.svg |
| Gnuplot source code |
|---|
set xrange [1:15]
set yrange [0.9:15900]
set logscale y
set xtics 1
set ytics 5
set grid
set key top left
$data <<EOF
1 0.900 0.950 1.000 1.050 1.100 1.150 1.200 1.250 1.300 1.350 1.400 1.450 1.500 1.550 1.600
2 4.457 4.213 4.000 3.812 3.645 3.495 3.361 3.240 3.130 3.030 2.939 2.855 2.778 2.707 2.641
3 1.835 1.894 1.953 2.012 2.070 2.127 2.184 2.241 2.297 2.353 2.408 2.462 2.515 2.568 2.621
4 5.695 5.449 5.226 5.024 4.839 4.671 4.516 4.374 4.244 4.124 4.013 3.910 3.815 3.726 3.643
5 2.245 2.322 2.400 2.479 2.558 2.638 2.719 2.799 2.880 2.961 3.042 3.123 3.203 3.283 3.362
6 9.118 8.575 8.085 7.642 7.242 6.879 6.550 6.251 5.978 5.730 5.503 5.296 5.105 4.930 4.769
7 2.072 2.164 2.262 2.365 2.473 2.586 2.704 2.826 2.953 3.083 3.218 3.356 3.498 3.643 3.790
8 23.351 20.876 18.702 16.796 15.129 13.672 12.400 11.287 10.314 9.462 8.714 8.056 7.476 6.963 6.509
9 1.458 1.524 1.598 1.683 1.779 1.888 2.010 2.147 2.300 2.470 2.659 2.867 3.095 3.346 3.619
10 185.204 155.399 128.980 106.046 86.522 70.189 56.733 45.789 36.980 29.945 24.358 19.935 16.436 13.667 11.471
11 1.061 1.073 1.089 1.109 1.135 1.168 1.212 1.268 1.341 1.435 1.557 1.713 1.915 2.174 2.508
12 2885.992 2702.359 2487.053 2240.142 1965.072 1669.656 1366.325 1071.048 800.691 569.377 385.213 248.892 154.780 93.729 56.084
13 1.005 1.005 1.005 1.006 1.007 1.008 1.010 1.012 1.016 1.023 1.034 1.054 1.087 1.148 1.258
14 15876.096 15842.207 15796.224 15732.849 15643.959 15516.831 15331.137 15053.927 14631.622 13978.667 12966.465 11429.205 9230.629 6448.472 3597.403
15 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.001 1.002 1.002 1.004
EOF
# plot $data using 1:2 with lines lw 2 title "0.90"
#replot $data using 1:3 with lines lw 2 title "0.95"
plot $data using 1:4 with lines lw 2 title "1.00"
replot $data using 1:5 with lines lw 2 title "1.05"
replot $data using 1:6 with lines lw 2 title "1.10"
replot $data using 1:7 with lines lw 2 title "1.15" #______________
replot $data using 1:8 with lines lw 2 title "1.20"
replot $data using 1:9 with lines lw 2 title "1.25"
replot $data using 1:10 with lines lw 2 title "1.30"
replot $data using 1:11 with lines lw 2 title "1.35"
#replot $data using 1:12 with lines lw 2 title "1.40"
#replot $data using 1:13 with lines lw 2 title "1.45"
#replot $data using 1:14 with lines lw 2 title "1.50"
#replot $data using 1:15 with lines lw 2 title "1.55"
#replot $data using 1:16 with lines lw 2 title "1.60"
pause -1
|
| C source code of the actual data |
|---|
#include <math.h>
#include <stdio.h>
#define iterMax 16
#define colMax 15
#define x0 0.9
#define xStep 0.05
int main(void)
{
int n;
int i;
long double x[colMax];
for (i=0; i<colMax; ++i)
x[i] = x0 + i * xStep;
for (n=1; n<iterMax; ++n) {
printf("%2d",n);
for (i=0; i<colMax; ++i)
printf(" %9.3Lf",x[i]);
printf("\n");
for (i=0; i<colMax; ++i)
x[i] = powl(1.0+1.0/x[i],n+1);
}
return 0;
}
|
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 18:00, 12 October 2020 |  | 3,475 × 2,045 (11 KB) | Jochen Burghardt (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.