Summary

You searched for: h3=11

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1

New Number: 5.83 |  AESZ: 316  |  Superseeker: 852/11 1678156/11  |  Hash: b8201d587a016cc013e2477aadb5c1ff  

Degree: 5

\(11^{2} \theta^4-2^{2} 3 11 x\left(364\theta^4+824\theta^3+599\theta^2+187\theta+22\right)-2^{5} x^{2}\left(62164\theta^4+84496\theta^3+12499\theta^2-6402\theta-1584\right)-2^{4} 3 x^{3}\left(484016\theta^4+474144\theta^3+366952\theta^2+161832\theta+27027\right)-2^{11} 3^{2} x^{4}(964\theta^2+1360\theta+669)(2\theta+1)^2-2^{16} 3^{4} x^{5}(2\theta+1)^2(2\theta+3)^2\)

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Coefficients of the holomorphic solution: 1, 24, 3240, 675600, 171901800, ...
--> OEIS
Normalized instanton numbers (n0=1): 852/11, 21572/11, 1678156/11, 15912512, 22956446184/11, ... ; Common denominator:...

Discriminant

\(-(2304z^3+1664z^2+432z-1)(11+192z)^2\)

Local exponents

≈\(-0.362258-0.240689I\) ≈\(-0.362258+0.240689I\)\(-\frac{ 11}{ 192}\)\(0\) ≈\(0.002294\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(1\)\(0\)\(1\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(\frac{ 3}{ 2}\)
\(2\)\(2\)\(4\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.83" from ...

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2

New Number: 8.32 |  AESZ: 317  |  Superseeker: 69/4 14365/12  |  Hash: cda8cce31025f51636125bea67a820d1  

Degree: 8

\(2^{4} \theta^4-2^{2} 3 x\left(162\theta^4+414\theta^3+335\theta^2+128\theta+20\right)+3^{3} x^{2}\left(1219\theta^4+10906\theta^3+18963\theta^2+11824\theta+2708\right)+3^{5} 5 x^{3}\left(922\theta^4+162\theta^3-6403\theta^2-6576\theta-1964\right)-3^{7} x^{4}\left(10358\theta^4+58054\theta^3+62251\theta^2+29672\theta+4907\right)-3^{9} 5 x^{5}\left(1519\theta^4-1262\theta^3+1371\theta^2+4264\theta+1802\right)+2 3^{11} 5 x^{6}\left(1727\theta^4+3702\theta^3+3085\theta^2+882\theta+17\right)-3^{13} 5^{2} x^{7}\left(239\theta^4+460\theta^3+314\theta^2+84\theta+6\right)-3^{16} 5^{2} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 15, 459, 19545, 1019259, ...
--> OEIS
Normalized instanton numbers (n0=1): 69/4, -30, 14365/12, 3015/2, 1376205/4, ... ; Common denominator:...

Discriminant

\(-(27z-1)(243z^3+2214z^2-117z+1)(-4-45z+405z^2)^2\)

Local exponents

≈\(-9.163702\)\(\frac{ 1}{ 18}-\frac{ 1}{ 90}\sqrt{ 105}\)\(0\) ≈\(0.010727\)\(\frac{ 1}{ 27}\) ≈\(0.041864\)\(\frac{ 1}{ 18}+\frac{ 1}{ 90}\sqrt{ 105}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(2\)\(4\)\(1\)

Note:

This operator has a second MUM-point at infininty corresponding to operator 8.31

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