1
New Number: 8.30 | AESZ: 314 | Superseeker: 229/4 297111/4 | Hash: 893692ba7eb3effcbc0c3b48d405456a
Degree: 8
\(2^{4} \theta^4-2^{2} x\left(1282\theta^4+2618\theta^3+1909\theta^2+600\theta+72\right)-3^{2} x^{2}\left(9503\theta^4+26810\theta^3+31755\theta^2+15944\theta+2936\right)+3^{4} x^{3}\left(15627\theta^4-18288\theta^3-91412\theta^2-53256\theta-9688\right)+2 3^{6} x^{4}\left(15106\theta^4+20300\theta^3-20421\theta^2-23443\theta-5907\right)-2^{2} 3^{8} x^{5}\left(2072\theta^4-18256\theta^3-2563\theta^2+4626\theta+1495\right)-2^{2} 3^{10} x^{6}\left(6204\theta^4+360\theta^3-281\theta^2+1017\theta+434\right)-2^{5} 3^{12} x^{7}(2\theta+1)(100\theta^3+162\theta^2+95\theta+21)+2^{8} 3^{14} x^{8}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 1926, 310860, 61060230, ... --> OEIS Normalized instanton numbers (n0=1): 229/4, 1293, 297111/4, 6150238, 2540085295/4, ... ; Common denominator:...
\((z-1)(11664z^3+3888z^2+324z-1)(-4-9z+648z^2)^2\)
| ≈\(-0.168156-0.022431I\) | ≈\(-0.168156+0.022431I\) | \(\frac{ 1}{ 144}-\frac{ 1}{ 144}\sqrt{ 129}\) | \(0\) | \(\frac{ 1}{ 18}2^(\frac{ 1}{ 3})+\frac{ 1}{ 36}2^(\frac{ 2}{ 3})-\frac{ 1}{ 9}\) | \(\frac{ 1}{ 144}+\frac{ 1}{ 144}\sqrt{ 129}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(2\) | \(4\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
New Number: 8.5 | AESZ: 173 | Superseeker: 11 -2434/3 | Hash: afa82ed9ee239bb5fcac960f8884db01
Degree: 8
\(\theta^4-x(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{6} x^{2}\left(55\theta^4+112\theta^3+155\theta^2+86\theta+15\right)-2^{6} 3^{2} x^{3}\left(119\theta^4-714\theta^3-2185\theta^2-1656\theta-444\right)+2^{12} 3^{2} x^{4}\left(92\theta^4+184\theta^3+98\theta^2+6\theta+9\right)+2^{12} 3^{4} x^{5}\left(119\theta^4+1190\theta^3+671\theta^2-96\theta-140\right)+2^{18} 3^{4} x^{6}\left(55\theta^4+108\theta^3+149\theta^2+108\theta+27\right)+2^{18} 3^{6} x^{7}(7\theta^2+7\theta+2)(17\theta^2+17\theta+6)+2^{24} 3^{8} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 12, 420, 17472, 828324, ... --> OEIS Normalized instanton numbers (n0=1): 11, 229/4, -2434/3, 7512, 54801, ... ; Common denominator:...
\((72z-1)(8z+1)(64z-1)(9z+1)(1+576z^2)^2\)
| \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 9}\) | \(0-\frac{ 1}{ 24}I\) | \(0\) | \(0+\frac{ 1}{ 24}I\) | \(\frac{ 1}{ 72}\) | \(\frac{ 1}{ 64}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(0\) | \(3\) | \(1\) | \(1\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(0\) | \(4\) | \(2\) | \(2\) | \(1\) |