Summary

You searched for: inst=-6

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1

New Number: 2.58 |  AESZ: 46  |  Superseeker: -6 -104  |  Hash: 2226ec115674e71c483ba2c0350e8adf  

Degree: 2

\(\theta^4-2 3 x(2\theta+1)^2(9\theta^2+9\theta+5)+2^{2} 3^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 30, 1782, 129900, 10463670, ...
--> OEIS
Normalized instanton numbers (n0=1): -6, -6, -104, 36, -4812, ... ; Common denominator:...

Discriminant

\((108z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 6}\)\(1\)
\(0\)\(\frac{ 5}{ 6}\)\(1\)
\(0\)\(1\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \iota$

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2

New Number: 2.67 |  AESZ: 245  |  Superseeker: -6 -170  |  Hash: 0ef0bca0dbecbedad92696fd7c0f9e42  

Degree: 2

\(\theta^4-2 3 x\left(36\theta^4+66\theta^3+61\theta^2+28\theta+5\right)+2^{2} 3^{2} x^{2}(3\theta+2)^2(6\theta+7)^2\)

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Coefficients of the holomorphic solution: 1, 30, 1764, 127776, 10248750, ...
--> OEIS
Normalized instanton numbers (n0=1): -6, -33, -170, -1029, -3246, ... ; Common denominator:...

Discriminant

\((108z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\infty\)
\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(0\)\(\frac{ 1}{ 6}\)\(\frac{ 2}{ 3}\)
\(0\)\(1\)\(\frac{ 7}{ 6}\)
\(0\)\(\frac{ 7}{ 6}\)\(\frac{ 7}{ 6}\)

Note:

This is operator "2.67" from ...

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3

New Number: 8.84 |  AESZ:  |  Superseeker: 1/5 224/5  |  Hash: 258fab6f0a4f132fe597fc6f30e54eea  

Degree: 8

\(5^{2} \theta^4+5 x\theta^2(-1-2\theta+107\theta^2)+2^{2} x^{2}\left(2174\theta^4+5942\theta^3+8569\theta^2+5200\theta+1200\right)+2^{2} 3^{2} x^{3}\left(308\theta^4-4248\theta^3-17051\theta^2-16785\theta-5280\right)-2^{4} 3^{2} x^{4}\left(7060\theta^4+39500\theta^3+69820\theta^2+52851\theta+14688\right)-2^{6} 3^{4} x^{5}\left(881\theta^4+3974\theta^3+8648\theta^2+7983\theta+2581\right)+2^{7} 3^{4} x^{6}\left(1192\theta^4+2376\theta^3-1132\theta^2-4185\theta-1926\right)+2^{8} 3^{6} x^{7}\left(68\theta^4+568\theta^3+1095\theta^2+811\theta+210\right)-2^{12} 3^{8} x^{8}\left((\theta+1)^4\right)\)

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Coefficients of the holomorphic solution: 1, 0, -12, 144, 324, ...
--> OEIS
Normalized instanton numbers (n0=1): 1/5, -6, 224/5, -448/5, -4334/5, ... ; Common denominator:...

Discriminant

\(-(9z-1)(576z^3+368z^2+16z+1)(-5-36z+72z^2)^2\)

Local exponents

≈\(-0.597246\)\(\frac{ 1}{ 4}-\frac{ 1}{ 12}\sqrt{ 19}\) ≈\(-0.020821-0.049733I\) ≈\(-0.020821+0.049733I\)\(0\)\(\frac{ 1}{ 9}\)\(\frac{ 1}{ 4}+\frac{ 1}{ 12}\sqrt{ 19}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(1\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(4\)\(2\)\(2\)\(0\)\(2\)\(4\)\(1\)

Note:

This is operator "8.84" from ...

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