1
New Number: 10.7 | AESZ: | Superseeker: 4 -628/9 | Hash: d5910f048831bb407eb8998c7c57e09f
Degree: 10
\(\theta^4-2^{2} x\left(48\theta^4+48\theta^3+45\theta^2+21\theta+4\right)+2^{6} x^{2}\left(261\theta^4+489\theta^3+590\theta^2+364\theta+93\right)-2^{6} x^{3}\left(13530\theta^4+35628\theta^3+50795\theta^2+36813\theta+10853\right)+2^{8} 3 x^{4}\left(38616\theta^4+128020\theta^3+206502\theta^2+165712\theta+53013\right)-2^{10} x^{5}\left(685404\theta^4+2714928\theta^3+4854121\theta^2+4193537\theta+1415126\right)+2^{13} x^{6}\left(1419108\theta^4+6542898\theta^3+12841310\theta^2+11823966\theta+4167463\right)-2^{14} x^{7}\left(8117226\theta^4+43045764\theta^3+92299521\theta^2+90336771\theta+33184985\right)+2^{16} x^{8}\left(15319683\theta^4+93106380\theta^3+218052374\theta^2+226725820\theta+86734943\right)-2^{19} 5^{2} x^{9}(2\theta+3)(171838\theta^3+939735\theta^2+1668155\theta+905358)+2^{22} 3 5^{4} 17^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 16, 292, 5728, 115012, ... --> OEIS Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...
\((12z-1)(18496z^3-2352z^2+84z-1)(16z-1)^2(400z^2-32z+1)^2\)
| \(0\) | ≈\(0.024764-0.009119I\) | ≈\(0.024764+0.009119I\) | \(\frac{ 1}{ 25}-\frac{ 3}{ 100}I\) | \(\frac{ 1}{ 25}+\frac{ 3}{ 100}I\) | \(\frac{ 1}{ 16}\) | ≈\(0.077634\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(\frac{ 5}{ 2}\) |
| \(0\) | \(2\) | \(2\) | \(4\) | \(4\) | \(1\) | \(2\) | \(2\) | \(3\) |
2
New Number: 8.28 | AESZ: 303 | Superseeker: 151/13 26293/13 | Hash: e081c85684dd16a72eeaf5a1b139b912
Degree: 8
\(13^{2} \theta^4-13 x\left(1505\theta^4+2746\theta^3+2127\theta^2+754\theta+104\right)+2^{2} x^{2}\left(22961\theta^4-2086\theta^3-55741\theta^2-41574\theta-9256\right)+2^{5} x^{3}\left(7524\theta^4+28098\theta^3+16131\theta^2+2691\theta-52\right)-2^{7} x^{4}\left(7241\theta^4+6214\theta^3+17522\theta^2+15423\theta+4146\right)-2^{8} x^{5}\left(6087\theta^4+1806\theta^3-3905\theta^2-3796\theta-1036\right)+2^{10} x^{6}\left(553\theta^4+4062\theta^3+4405\theta^2+1752\theta+220\right)+2^{14} x^{7}\left(82\theta^4+230\theta^3+275\theta^2+160\theta+37\right)+2^{18} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 8, 292, 15776, 1030036, ... --> OEIS Normalized instanton numbers (n0=1): 151/13, 1436/13, 26293/13, 719465/13, 24184128/13, ... ; Common denominator:...
\((z-1)(64z^3+304z^2+108z-1)(-13+44z+64z^2)^2\)
| ≈\(-4.362346\) | \(-\frac{ 11}{ 32}-\frac{ 1}{ 32}\sqrt{ 329}\) | ≈\(-0.396684\) | \(0\) | ≈\(0.009029\) | \(-\frac{ 11}{ 32}+\frac{ 1}{ 32}\sqrt{ 329}\) | \(1\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) | \(1\) |
| \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(3\) | \(1\) | \(1\) |
| \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(4\) | \(2\) | \(1\) |