File:Lagrange polynomials for continuations of sequence 1,2,3.gif
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Summary
| Description |
English: Lagrange polynomials and their graphs for ten possible continuations (0 to 9) of the sequence 1,2,3; each polynomial evaluates to 1,2,3, and the continuation at input 1,2,3, and 4, respectively; the "correct" continuation 4 leads to the polynomial of least degree |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
Lagrange polynomials as txt
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2 3 2 19
1, 2, 3, 0 - - x + 4x - -- x + 4
3 3
1 3 2 9
1, 2, 3, 1 - - x + 3x - - x + 3
2 2
1 3 2 8
1, 2, 3, 2 - - x + 2x - - x + 2
3 3
1 3 2 5
1, 2, 3, 3 - - x + x - - x + 1
6 6
1, 2, 3, 4 x
1 3 2 17
1, 2, 3, 5 - x - x + -- x - 1
6 6
1 3 2 14
1, 2, 3, 6 - x - 2x + -- x - 2
3 3
1 3 2 13
1, 2, 3, 7 - x - 3x + -- x - 3
2 2
2 3 2 25
1, 2, 3, 8 - x - 4x + -- x - 4
3 3
5 3 2 61
1, 2, 3, 9 - x - 5x + -- x - 5
6 6
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Gnuplot source
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set xrange [0.9:4.1]
plot -2./3.*x*x*x +4.*x*x -19./3.*x +4. title "" with lines
replot -1./2.*x*x*x +3.*x*x -9./2.*x +3. title "" with lines
replot -1./3.*x*x*x +2.*x*x -8./3.*x +2. title "" with lines
replot -1./6.*x*x*x +x*x -5./6.*x +1. title "" with lines
replot x title "" with lines
replot 1./6.*x*x*x -x*x +17./6.*x -1. title "" with lines
replot 1./3.*x*x*x -2.*x*x +14./3.*x -2. title "" with lines
replot 1./2.*x*x*x -3.*x*x +13./2.*x -3. title "" with lines
replot 2./3.*x*x*x -4.*x*x +25./3.*x -4. title "" with lines
replot 5./6.*x*x*x -5.*x*x +61./6.*x -5. title "" with lines
pause -1
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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- 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.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:00, 7 November 2013 | | 1,649 × 959 (67 KB) | Jochen Burghardt | User created page with UploadWizard |
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