1
New Number: 5.109 | AESZ: 373 | Superseeker: 50 68472 | Hash: 8b0fbfc0016c3fb02fd42d4ff919e0f8
Degree: 5
\(\theta^4-2 x\left(190\theta^4+308\theta^3+227\theta^2+73\theta+9\right)+2^{2} x^{2}\left(4780\theta^4+6304\theta^3+2395\theta^2+642\theta+135\right)-2^{4} 3 x^{3}\left(6700\theta^4+8472\theta^3+7607\theta^2+3615\theta+648\right)+2^{7} 3^{2} x^{4}(2\theta+1)(760\theta^3+1464\theta^2+1211\theta+375)-2^{10} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 18, 1782, 276660, 52396470, ... --> OEIS Normalized instanton numbers (n0=1): 50, 1299, 68472, 5536032, 555252324, ... ; Common denominator:...
\(-(-1+324z)(24z-1)^2(4z-1)^2\)
| \(0\) | \(\frac{ 1}{ 324}\) | \(\frac{ 1}{ 24}\) | \(\frac{ 1}{ 4}\) | \(\infty\) |
|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(\frac{ 1}{ 2}\) |
| \(0\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(1\) | \(3\) | \(\frac{ 1}{ 2}\) | \(1\) |
| \(0\) | \(2\) | \(4\) | \(1\) | \(\frac{ 3}{ 2}\) |
2
New Number: 6.21 | AESZ: | Superseeker: 1 11 | Hash: 319d6b2f1541de5252840442cc6f8dcd
Degree: 6
\(\theta^4+x\left(6+27\theta+47\theta^2+40\theta^3+20\theta^4\right)-x^{2}(143\theta^2+286\theta+120)(\theta+1)^2-2 3^{2} x^{3}(\theta+2)(\theta+1)(291\theta^2+873\theta+766)-2^{2} 3^{3} 5 x^{4}(\theta+3)(\theta+1)(41\theta^2+164\theta+196)+2^{3} 3^{3} 5^{2} x^{5}(\theta+4)(\theta+1)(29\theta^2+145\theta+150)+2^{5} 3^{5} 5^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)\)
Maple LaTexCoefficients of the holomorphic solution: 1, -6, 60, -480, 5040, ... --> OEIS Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...
\((6z-1)(15z-1)(9z+1)(12z+1)(10z+1)^2\)
| \(0\) | \(\frac{ 1}{ 6}\) | \(\infty\) | \(-\frac{ 1}{ 12}\) | \(-\frac{ 1}{ 10}\) | \(-\frac{ 1}{ 9}\) | \(\frac{ 1}{ 15}\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(1\) | \(0\) | \(0\) | \(0\) | \(0\) |
| \(0\) | \(1\) | \(2\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(1\) | \(4\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(1\) |
| \(0\) | \(2\) | \(5\) | \(2\) | \(1\) | \(2\) | \(2\) |
3
New Number: 7.10 | AESZ: | Superseeker: 1 11 | Hash: b1c277f62ba740f9f7e0371ba53e4194
Degree: 7
\(\theta^4-x\left(76\theta^4+80\theta^3+73\theta^2+33\theta+6\right)+x^{2}\left(2209\theta^4+4228\theta^3+4745\theta^2+2726\theta+648\right)-2 3^{2} x^{3}\left(1735\theta^4+4646\theta^3+6099\theta^2+4072\theta+1124\right)+2^{2} 3^{3} x^{4}\left(2085\theta^4+7388\theta^3+11695\theta^2+9140\theta+2844\right)-2^{3} 3^{3} x^{5}(\theta+1)(3707\theta^3+14055\theta^2+20242\theta+10704)+2^{6} 3^{5} x^{6}(\theta+1)(\theta+2)(86\theta^2+285\theta+262)-2^{7} 3^{8} x^{7}(\theta+1)(\theta+2)^2(\theta+3)\)
Maple LaTexCoefficients of the holomorphic solution: 1, 6, 60, 816, 13104, ... --> OEIS Normalized instanton numbers (n0=1): 1, 13/4, 11, 50, 1674/5, ... ; Common denominator:...
\(-(3z-1)(18z-1)(27z-1)(12z-1)^2(-1+2z)^2\)
| \(0\) | \(\frac{ 1}{ 27}\) | \(\frac{ 1}{ 18}\) | \(\frac{ 1}{ 3}\) | \(\frac{ 1}{ 2}\) | \(\frac{ 1}{ 12}\) | \(\infty\) |
|---|---|---|---|---|---|---|
| \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(0\) | \(1\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(1\) | \(2\) |
| \(0\) | \(1\) | \(1\) | \(1\) | \(\frac{ 1}{ 2}\) | \(3\) | \(2\) |
| \(0\) | \(2\) | \(2\) | \(2\) | \(1\) | \(4\) | \(3\) |