1
New Number: 12.3 | AESZ: | Superseeker: -12/5 444/5 | Hash: 45726409a4c817f929c9e6e49b33a941
Degree: 12
\(5^{2} \theta^4+2^{2} 5 x\left(4\theta^4+56\theta^3+53\theta^2+25\theta+5\right)-2^{4} x^{2}\left(976\theta^4+6208\theta^3+9016\theta^2+6360\theta+1985\right)+2^{8} x^{3}\left(832\theta^4-2304\theta^3-11276\theta^2-12780\theta-5495\right)+2^{13} x^{4}\left(176\theta^4+4672\theta^3+16244\theta^2+19860\theta+9145\right)-2^{16} x^{5}\left(1824\theta^4+8448\theta^3+1052\theta^2-6884\theta-5771\right)+2^{21} x^{6}\left(432\theta^4+192\theta^3-3816\theta^2-9540\theta-5869\right)+2^{24} x^{7}\left(704\theta^4+10048\theta^3+21804\theta^2+22348\theta+7847\right)-2^{29} x^{8}\left(472\theta^4+2176\theta^3+7884\theta^2+11644\theta+5965\right)+2^{32} x^{9}\left(336\theta^4+672\theta^3+1144\theta^2+2904\theta+2145\right)+2^{36} x^{10}\left(368\theta^4+1216\theta^3+1304\theta^2-240\theta-697\right)-2^{44} x^{11}(2\theta+3)(4\theta^3+28\theta^2+51\theta+28)-2^{46} x^{12}\left((2\theta+3)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, 108, -912, 21484, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, 103/5, 444/5, 1148/5, -6704, ... ; Common denominator:...
\(-(-1-16z+256z^2)(16z+1)^2(16z-1)^2(8192z^3+768z^2-32z+5)^2\)
| ≈\(-0.148005\) | \(-\frac{ 1}{ 16}\) | \(\frac{ 1}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\) | \(0\) | ≈\(0.027128-0.058206I\) | ≈\(0.027128+0.058206I\) | \(\frac{ 1}{ 16}\) | \(\frac{ 1}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\) | \(\infty\) |
|---|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 2}\) |
| \(1\) | \(0\) | \(1\) | \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(3\) | \(1\) | \(1\) | \(0\) | \(3\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) | \(\frac{ 3}{ 2}\) |
| \(4\) | \(1\) | \(2\) | \(0\) | \(4\) | \(4\) | \(1\) | \(2\) | \(\frac{ 3}{ 2}\) |
2
New Number: 8.39 | AESZ: | Superseeker: -12/5 136/3 | Hash: c1330764e09752f7bb8e86b15541c588
Degree: 8
\(5^{2} \theta^4+2 3 5 x\left(51\theta^4+84\theta^3+72\theta^2+30\theta+5\right)+2^{2} 3 x^{2}\left(3297\theta^4+10236\theta^3+13562\theta^2+8110\theta+1830\right)+2^{2} 3^{3} x^{3}\left(3866\theta^4+14088\theta^3+21137\theta^2+14355\theta+3600\right)+2^{3} 3^{3} x^{4}\left(11680\theta^4+38792\theta^3+45641\theta^2+24205\theta+4854\right)+2^{4} 3^{5} x^{5}\left(2624\theta^4+8240\theta^3+8275\theta^2+2971\theta+216\right)+2^{5} 3^{5} x^{6}\left(3248\theta^4+8832\theta^3+9739\theta^2+4803\theta+882\right)+2^{7} 3^{7} x^{7}\left(144\theta^4+384\theta^3+428\theta^2+233\theta+51\right)+2^{9} 3^{7} x^{8}(4\theta+3)(\theta+1)^2(4\theta+5)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 54, -348, -3690, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, -21/5, 136/3, -1743/10, -1056/5, ... ; Common denominator:...
\((1+54z+1152z^2+6048z^3+3456z^4)(5+18z+72z^2)^2\)
| ≈\(-1.540068\) | ≈\(-0.152177\) | \(-\frac{ 1}{ 8}-\frac{ 1}{ 24}\sqrt{ 31}I\) | \(-\frac{ 1}{ 8}+\frac{ 1}{ 24}\sqrt{ 31}I\) | ≈\(-0.028878\) | ≈\(-0.028878\) | \(0\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 3}{ 4}\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(3\) | \(3\) | \(1\) | \(1\) | \(0\) | \(1\) |
| \(2\) | \(2\) | \(4\) | \(4\) | \(2\) | \(2\) | \(0\) | \(\frac{ 5}{ 4}\) |
3
New Number: 8.45 | AESZ: | Superseeker: -12/5 -20 | Hash: 52e4f6959f297529016ddef66a399c12
Degree: 8
\(5^{2} \theta^4+2^{2} 5 x\left(19\theta^4+86\theta^3+73\theta^2+30\theta+5\right)+2^{4} x^{2}\left(709\theta^4+4252\theta^3+7339\theta^2+4830\theta+1165\right)-2^{8} x^{3}\left(420\theta^4+114\theta^3-3294\theta^2-3960\theta-1325\right)-2^{10} x^{4}\left(949\theta^4+6782\theta^3+11350\theta^2+7719\theta+1889\right)+2^{12} x^{5}\left(1315\theta^4+4282\theta^3+7199\theta^2+5744\theta+1691\right)+2^{14} x^{6}\left(613\theta^4+1560\theta^3+973\theta^2-216\theta-249\right)+2^{18} x^{7}\left(11\theta^4-2\theta^3-40\theta^2-39\theta-11\right)-2^{20} x^{8}\left((\theta+1)^4\right)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -4, -4, 464, -4244, ... --> OEIS Normalized instanton numbers (n0=1): -12/5, -83/5, -20, 3941/20, -13872/5, ... ; Common denominator:...
\(-(8z+1)(128z^3-624z^2-20z-1)(-5+32z+32z^2)^2\)
| \(-\frac{ 1}{ 2}-\frac{ 1}{ 8}\sqrt{ 26}\) | \(-\frac{ 1}{ 8}\) | ≈\(-0.016083-0.036516I\) | ≈\(-0.016083+0.036516I\) | \(0\) | \(-\frac{ 1}{ 2}+\frac{ 1}{ 8}\sqrt{ 26}\) | ≈\(4.907166\) | \(\infty\) |
|---|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(1\) | \(1\) | \(1\) | \(1\) | \(0\) | \(1\) | \(1\) | \(1\) |
| \(3\) | \(1\) | \(1\) | \(1\) | \(0\) | \(3\) | \(1\) | \(1\) |
| \(4\) | \(2\) | \(2\) | \(2\) | \(0\) | \(4\) | \(2\) | \(1\) |