Summary

You searched for: sol=26

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1

New Number: 10.3 |  AESZ:  |  Superseeker: 2 421/9  |  Hash: 5219414e025733d8e128028821370b4b  

Degree: 10

\(\theta^4-x\left(321\theta^4+258\theta^3+258\theta^2+129\theta+26\right)+x^{2}\left(74028\theta^3+14112+55150\theta+89219\theta^2+46467\theta^4\right)-2^{3} x^{3}\left(499260\theta^4+1184748\theta^3+1665809\theta^2+1187841\theta+345452\right)+2^{4} 3 x^{4}\left(4702665\theta^4+14805730\theta^3+23754818\theta^2+18867201\theta+5979118\right)-2^{6} x^{5}\left(136927125\theta^4+537349854\theta^3+968406086\theta^2+839579917\theta+283906432\right)+2^{6} x^{6}\left(3697617171\theta^4+17401686816\theta^3+34821823585\theta^2+32540314464\theta+11600569724\right)-2^{9} x^{7}\left(8571324186\theta^4+47135706036\theta^3+103830096399\theta^2+103713883221\theta+38684901782\right)+2^{12} x^{8}\left(13055773347\theta^4+82367586444\theta^3+198438600506\theta^2+210671505052\theta+81797663483\right)-2^{16} 137 x^{9}(2\theta+3)(21527774\theta^3+121431015\theta^2+220937755\theta+121634574)+2^{20} 3 73^{2} 137^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

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Coefficients of the holomorphic solution: 1, 26, 730, 21320, 638506, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -3/2, 421/9, -519/2, 285, ... ; Common denominator:...

Discriminant

\((24z-1)(42632z^3-3675z^2+105z-1)(32z-1)^2(1096z^2-64z+1)^2\)

Local exponents

\(0\) ≈\(0.025716-0.003646I\) ≈\(0.025716+0.003646I\)\(\frac{ 4}{ 137}-\frac{ 3}{ 548}\sqrt{ 2}I\)\(\frac{ 4}{ 137}+\frac{ 3}{ 548}\sqrt{ 2}I\)\(\frac{ 1}{ 32}\) ≈\(0.034771\)\(\frac{ 1}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(3\)

Note:

This is operator "10.3" from ...

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2

New Number: 6.26 |  AESZ:  |  Superseeker: 58/43 1024/43  |  Hash: 38ef7a13fad0ecbb53ba25dafe26b113  

Degree: 6

\(43^{2} \theta^4-43 x\left(830\theta^4+1750\theta^3+1434\theta^2+559\theta+86\right)-x^{2}\left(1342738\theta^3+368510+1383525\theta+354697\theta^4+2007703\theta^2\right)-x^{3}\left(2348230+6951423\theta+774028\theta^4+3928308\theta^3+7763518\theta^2\right)-3 5 x^{4}\left(44423\theta^4+264028\theta^3+597368\theta^2+599643\theta+221430\right)-2 3^{2} 5^{2} x^{5}(\theta+2)(\theta+1)(533\theta^2+1694\theta+1290)-3^{3} 5^{3} x^{6}(3\theta+5)(3\theta+4)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: 1, 2, 26, 344, 5650, ...
--> OEIS
Normalized instanton numbers (n0=1): 58/43, 211/43, 1024/43, 7544/43, 64880/43, ... ; Common denominator:...

Discriminant

\(-(5z+1)(27z-1)(15z+43)^2(z+1)^2\)

Local exponents

\(-\frac{ 43}{ 15}\)\(-1\)\(-\frac{ 1}{ 5}\)\(0\)\(\frac{ 1}{ 27}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(\frac{ 4}{ 3}\)
\(3\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(\frac{ 5}{ 3}\)
\(4\)\(1\)\(2\)\(0\)\(2\)\(2\)

Note:

This is operator "6.26" from ...

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