Summary

You searched for: sol=163

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1

New Number: 8.22 |  AESZ: 284  |  Superseeker: 241/38 8729/19  |  Hash: dbe506beab1f66a0b331f15c91b7fcde  

Degree: 8

\(2^{2} 19^{2} \theta^4-2 19 x\left(3014\theta^4+5878\theta^3+4725\theta^2+1786\theta+266\right)+x^{2}\left(402002+1810054\theta+3057079\theta^2+2305502\theta^3+689717\theta^4\right)-x^{3}\left(1576582+6295992\theta+9142457\theta^2+5812350\theta^3+1438808\theta^4\right)+x^{4}\left(663471+3375833\theta+6297445\theta^2+5075392\theta^3+1395491\theta^4\right)+x^{5}\left(52928-604005\theta-2407768\theta^2-2657224\theta^3-834163\theta^4\right)-x^{6}\left(4832-148359\theta-572576\theta^2-692484\theta^3-277543\theta^4\right)-11 x^{7}\left(4625\theta^4+9100\theta^3+6395\theta^2+1845\theta+178\right)-11^{2} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 7, 163, 5767, 247651, ...
--> OEIS
Normalized instanton numbers (n0=1): 241/38, 1353/38, 8729/19, 150334/19, 6399445/38, ... ; Common denominator:...

Discriminant

\(-(-1+78z-374z^2+425z^3+z^4)(38-25z+11z^2)^2\)

Local exponents

\(0\)\(\frac{ 25}{ 22}-\frac{ 1}{ 22}\sqrt{ 1047}I\)\(\frac{ 25}{ 22}+\frac{ 1}{ 22}\sqrt{ 1047}I\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(3\)\(3\)\(1\)\(1\)
\(0\)\(4\)\(4\)\(2\)\(1\)

Note:

This operator has a second MUM-point at infinity, corresponding to operator 8.23

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2

New Number: 9.6 |  AESZ:  |  Superseeker: 95/102 1421/102  |  Hash: 04982735f3d6178049251771352a0277  

Degree: 9

\(2^{2} 3^{2} 17^{2} \theta^4-2 3 17 x\left(1238\theta^4+2434\theta^3+1931\theta^2+714\theta+102\right)-x^{2}\left(1905719\theta^4+7435898\theta^3+11481377\theta^2+8054838\theta+2175150\right)-x^{3}\left(65375064\theta+31069026\theta^3+4568070\theta^4+22153074+70031651\theta^2\right)+x^{4}\left(4512344\theta^4-46914039-80101802\theta^2-111691663\theta-9395414\theta^3\right)+x^{5}\left(36577126+121266438\theta^3+23432568\theta^4+137186363\theta+194777323\theta^2\right)+x^{6}\left(69502656\theta^3-1312570+57037497\theta+121320734\theta^2+4255715\theta^4\right)-3 13 x^{7}\left(877789\theta^4+3969932\theta^3+7763293\theta^2+7084011\theta+2438016\right)-3^{2} 5 13^{2} x^{8}(\theta+1)(1514\theta^3+4164\theta^2+3373\theta+681)+3^{3} 5^{2} 13^{3} x^{9}(3\theta+5)(3\theta+4)(\theta+2)(\theta+1)\)

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Coefficients of the holomorphic solution: 1, 1, 17, 163, 2233, ...
--> OEIS
Normalized instanton numbers (n0=1): 95/102, 58/17, 1421/102, 1451/17, 31474/51, ... ; Common denominator:...

Discriminant

\((1-12z-181z^2-510z^3-328z^4+351z^5)(-102+7z+195z^2)^2\)

Local exponents

\(-\frac{ 7}{ 390}-\frac{ 1}{ 390}\sqrt{ 79609}\)\(0\)\(-\frac{ 7}{ 390}+\frac{ 1}{ 390}\sqrt{ 79609}\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(\frac{ 4}{ 3}\)
\(3\)\(0\)\(3\)\(1\)\(\frac{ 5}{ 3}\)
\(4\)\(0\)\(4\)\(2\)\(2\)

Note:

This is operator "9.6" from ...

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