1
New Number: 12.6 | AESZ: | Superseeker: 5 953/3 | Hash: 4ea78627bfc56ef9555d9b6b3c949e7a
Degree: 12
\(\theta^4-x\theta(5\theta^3+46\theta^2+29\theta+6)-2 3 x^{2}\left(258\theta^4+1038\theta^3+1387\theta^2+818\theta+192\right)-2^{2} 3^{3} x^{3}\left(381\theta^4+1664\theta^3+2804\theta^2+2126\theta+624\right)-2^{4} 3^{3} x^{4}\left(1231\theta^4+5927\theta^3+11019\theta^2+9266\theta+3000\right)-2^{4} 3^{4} x^{5}\left(2621\theta^4+16730\theta^3+39069\theta^2+35141\theta+11748\right)-2^{5} 3^{5} x^{6}\left(150\theta^4+11268\theta^3+45560\theta^2+50253\theta+18756\right)+2^{6} 3^{7} x^{7}\left(1024\theta^4+800\theta^3-8483\theta^2-13641\theta-6108\right)+2^{8} 3^{7} x^{8}\left(1724\theta^4+6608\theta^3+1047\theta^2-7027\theta-4488\right)+2^{11} 3^{8} x^{9}\left(74\theta^4+1416\theta^3+1889\theta^2+687\theta-81\right)-2^{13} 3^{10} x^{10}\left(26\theta^4-16\theta^3-125\theta^2-128\theta-39\right)-2^{14} 3^{11} x^{11}(\theta+1)(16\theta^3+40\theta^2+31\theta+6)-2^{16} 3^{11} x^{12}(\theta+2)(\theta+1)(2\theta+3)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, 1344, 48600, ... --> OEIS Normalized instanton numbers (n0=1): 5, 83/2, 953/3, 5319, 97812, ... ; Common denominator:...
\(-(4z+1)(12z+1)(3z+1)(1728z^3+864z^2+36z-1)(-1-6z-36z^2+432z^3)^2\)
| ≈\(-0.450956\) | \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 12}\) | ≈\(-0.067934\) | ≈\(-0.061146-0.08671I\) | ≈\(-0.061146+0.08671I\) | \(0\) | ≈\(0.01889\) | ≈\(0.205625\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(3\) | \(3\) | \(0\) | \(1\) | \(3\) | \(\frac{ 3}{ 2}\) |
| \(2\) | \(2\) | \(2\) | \(2\) | \(2\) | \(4\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) |
2
New Number: 8.21 | AESZ: 251 | Superseeker: -9 -3145/3 | Hash: dd2b60d18804c72129ba319fc8b50023
Degree: 8
\(\theta^4-3 x\theta(-2-11\theta-18\theta^2+27\theta^3)-2 3^{2} x^{2}\left(39\theta^4+480\theta^3+474\theta^2+276\theta+64\right)+2^{3} 3^{4} x^{3}\left(348\theta^4+1152\theta^3+1759\theta^2+1110\theta+260\right)-2^{3} 3^{5} x^{4}\left(3420\theta^4+15912\theta^3+28437\theta^2+20544\theta+5296\right)+2^{4} 3^{7} x^{5}\left(1125\theta^4+12546\theta^3+31089\theta^2+26448\theta+7480\right)+2^{5} 3^{9} x^{6}\left(1395\theta^4+3240\theta^3-3378\theta^2-7146\theta-2696\right)-2^{7} 3^{11} x^{7}\left(351\theta^4+2646\theta^3+4767\theta^2+3309\theta+800\right)-2^{7} 3^{13} x^{8}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 72, -1440, 48600, ... --> OEIS Normalized instanton numbers (n0=1): -9, -27/4, -3145/3, -20907/4, -327348, ... ; Common denominator:...
\(-(54z+1)(27z-1)(432z^2-36z+1)(-1+36z+324z^2)^2\)
| \(-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 2}\) | \(-\frac{ 1}{ 54}\) | \(0\) | \(-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 2}\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 2}{ 3}\) |
| \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 5}{ 6}\) |
| \(3\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 7}{ 6}\) |
| \(4\) | \(2\) | \(0\) | \(4\) | \(2\) | \(2\) | \(2\) | \(\frac{ 4}{ 3}\) |