1
New Number: 8.80 | AESZ: | Superseeker: -28/3 2764/3 | Hash: 01b1872abfd55652952ae535920a40fe
Degree: 8
\(3^{2} \theta^4+2^{2} 3 x\left(148\theta^4+248\theta^3+223\theta^2+99\theta+18\right)+2^{7} x^{2}\left(1124\theta^4+3080\theta^3+4211\theta^2+2709\theta+675\right)+2^{12} x^{3}\left(1684\theta^4+4872\theta^3+7059\theta^2+5373\theta+1530\right)+2^{17} x^{4}\left(1828\theta^4+4952\theta^3+5125\theta^2+2799\theta+599\right)+2^{23} x^{5}\left(720\theta^4+1992\theta^3+2102\theta^2+691\theta-13\right)+2^{29} x^{6}\left(200\theta^4+504\theta^3+669\theta^2+390\theta+83\right)+2^{35} x^{7}\left(40\theta^4+104\theta^3+118\theta^2+66\theta+15\right)+2^{43} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -24, 872, -37248, 1740456, ... --> OEIS Normalized instanton numbers (n0=1): -28/3, 49/3, 2764/3, 13414, 44384, ... ; Common denominator:...
\((16z+1)(32z+1)(64z+1)^2(2048z^2+32z+3)^2\)
| \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 64}\) | \(-\frac{ 1}{ 128}-\frac{ 1}{ 128}\sqrt{ 23}I\) | \(-\frac{ 1}{ 128}+\frac{ 1}{ 128}\sqrt{ 23}I\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(3\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(1\) | \(4\) | \(4\) | \(0\) | \(1\) |
2
New Number: 9.2 | AESZ: | Superseeker: 9/7 49/3 | Hash: 356d4564e48d7a04e815fa223b6ccc46
Degree: 9
\(7^{2} \theta^4+7 x\theta(165\theta^3-102\theta^2-65\theta-14)-2^{3} x^{2}\left(920\theta^4+11726\theta^3+15277\theta^2+9478\theta+2352\right)-2^{4} 3^{2} x^{3}\left(4035\theta^4+19554\theta^3+29157\theta^2+20706\theta+5761\right)-2^{8} 3^{2} x^{4}\left(4156\theta^4+17951\theta^3+28198\theta^2+21045\theta+6096\right)-2^{11} 3^{3} x^{5}\left(1538\theta^4+6560\theta^3+10755\theta^2+8234\theta+2420\right)-2^{13} 3^{4} x^{6}\left(695\theta^4+3051\theta^3+5285\theta^2+4191\theta+1259\right)-2^{14} 3^{5} x^{7}\left(385\theta^4+1802\theta^3+3319\theta^2+2754\theta+855\right)-2^{18} 3^{6} x^{8}(\theta+1)^2(15\theta^2+48\theta+43)-2^{20} 3^{7} x^{9}(\theta+1)^2(\theta+2)^2\)
Maple LaTexCoefficients of the holomorphic solution: 1, 0, 24, 144, 3240, ... --> OEIS Normalized instanton numbers (n0=1): 9/7, 47/7, 49/3, 1370/7, 10063/7, ... ; Common denominator:...
\(-(8z+1)(24z-1)(3z+1)(4z+1)(12z+1)(7+72z+288z^2)^2\)
| \(-\frac{ 1}{ 3}\) | \(-\frac{ 1}{ 4}\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 5}I\) | \(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 5}I\) | \(-\frac{ 1}{ 12}\) | \(0\) | \(\frac{ 1}{ 24}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(1\) | \(3\) | \(1\) | \(0\) | \(1\) | \(2\) |
| \(2\) | \(2\) | \(4\) | \(2\) | \(4\) | \(2\) | \(0\) | \(2\) | \(2\) |