1
New Number: 10.2 | AESZ: | Superseeker: 4 2252/9 | Hash: 4a65f8c6ad1f8eaf4aa56879ebb94205
Degree: 10
\(\theta^4+2^{2} x\left(69\theta^4+42\theta^3+45\theta^2+24\theta+5\right)+2^{4} x^{2}\left(2097\theta^4+2748\theta^3+3311\theta^2+1990\theta+489\right)+2^{8} x^{3}\left(9240\theta^4+19254\theta^3+26269\theta^2+17979\theta+5020\right)+2^{10} 3 x^{4}\left(34845\theta^4+101230\theta^3+156798\theta^2+120187\theta+36857\right)+2^{12} x^{5}\left(792225\theta^4+2972406\theta^3+5205467\theta^2+4394830\theta+1449907\right)+2^{14} x^{6}\left(4064601\theta^4+18714936\theta^3+36737137\theta^2+33711480\theta+11807867\right)+2^{18} x^{7}\left(3474333\theta^4+18927498\theta^3+41213301\theta^2+40674636\theta+14985820\right)+2^{20} x^{8}\left(7544547\theta^4+47365644\theta^3+113299226\theta^2+119329996\theta+45950951\right)+2^{24} 23 x^{9}(2\theta+3)(50786\theta^3+284985\theta^2+515497\theta+282264)+2^{28} 3 7^{2} 23^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -20, 436, -9872, 228292, ... --> OEIS Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...
\((24z+1)(8z+1)(784z^2+52z+1)(32z+1)^2(736z^2+64z+1)^2\)
\(-\frac{ 1}{ 8}\) | \(-\frac{ 1}{ 23}-\frac{ 3}{ 184}\sqrt{ 2}\) | \(-\frac{ 1}{ 24}\) | \(-\frac{ 13}{ 392}-\frac{ 3}{ 392}\sqrt{ 3}I\) | \(-\frac{ 13}{ 392}+\frac{ 3}{ 392}\sqrt{ 3}I\) | \(-\frac{ 1}{ 32}\) | \(-\frac{ 1}{ 23}+\frac{ 3}{ 184}\sqrt{ 2}\) | \(0\) | \(\infty\) |
---|---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(0\) | \(\frac{ 3}{ 2}\) |
\(1\) | \(3\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(0\) | \(\frac{ 5}{ 2}\) |
\(2\) | \(4\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(0\) | \(3\) |
2
New Number: 12.5 | AESZ: | Superseeker: 4 2252/9 | Hash: bb257a283455fdd1fa17fef9649505e3
Degree: 12
\(\theta^4+2^{2} x\left(43\theta^4+22\theta^3+25\theta^2+14\theta+3\right)+2^{4} x^{2}\left(753\theta^4+924\theta^3+1107\theta^2+622\theta+141\right)+2^{7} x^{3}\left(3377\theta^4+7218\theta^3+9261\theta^2+5764\theta+1455\right)+2^{10} x^{4}\left(7570\theta^4+24718\theta^3+34375\theta^2+21933\theta+5310\right)+2^{12} 3^{2} x^{5}\left(901\theta^4+5118\theta^3+5777\theta^2-84\theta-1829\right)-2^{14} 3^{2} x^{6}\left(7783\theta^4+33872\theta^3+83851\theta^2+107556\theta+49489\right)-2^{17} 3^{3} x^{7}\left(4895\theta^4+28154\theta^3+69267\theta^2+83564\theta+36929\right)-2^{20} 3^{4} x^{8}\left(44\theta^4+528\theta^3+247\theta^2+240\theta+274\right)+2^{23} 3^{5} x^{9}\left(664\theta^4+4760\theta^3+13781\theta^2+17353\theta+7679\right)+2^{26} 3^{6} x^{10}(\theta+1)(109\theta^3+651\theta^2+1373\theta+933)-2^{29} 3^{7} x^{11}(\theta+1)(\theta+2)(27\theta^2+153\theta+199)-2^{33} 3^{9} x^{12}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -12, 180, -2736, 42948, ... --> OEIS Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...
\(-(16z+1)(432z^2+36z+1)(24z+1)^2(288z^2+48z+1)^2(8z-1)^3\)
\(-\frac{ 1}{ 12}-\frac{ 1}{ 24}\sqrt{ 2}\) | \(-\frac{ 1}{ 16}\) | \(-\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I\) | \(-\frac{ 1}{ 24}\) | \(-\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I\) | \(-\frac{ 1}{ 12}+\frac{ 1}{ 24}\sqrt{ 2}\) | \(0\) | \(\frac{ 1}{ 8}\) | \(\infty\) |
---|---|---|---|---|---|---|---|---|
\(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
\(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) | \(0\) | \(\frac{ 1}{ 2}\) | \(2\) |
\(3\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(3\) | \(0\) | \(\frac{ 3}{ 2}\) | \(2\) |
\(4\) | \(2\) | \(2\) | \(1\) | \(2\) | \(4\) | \(0\) | \(2\) | \(3\) |