Summary

You searched for: inst=45

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1

New Number: 2.29 |  AESZ: 142  |  Superseeker: 45 27735  |  Hash: 85c2c2d8111a859d4cc03e8892c56af9  

Degree: 2

\(\theta^4-3^{2} x(3\theta+1)(3\theta+2)(18\theta^2+18\theta+7)+3^{8} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)\)

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Coefficients of the holomorphic solution: 1, 126, 44550, 20447280, 10600093350, ...
--> OEIS
Normalized instanton numbers (n0=1): 45, -3465/4, 27735, -1156005, 55721970, ... ; Common denominator:...

Discriminant

\((729z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 729}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 3}\)
\(0\)\(\frac{ 1}{ 3}\)\(\frac{ 2}{ 3}\)
\(0\)\(\frac{ 2}{ 3}\)\(\frac{ 4}{ 3}\)
\(0\)\(1\)\(\frac{ 5}{ 3}\)

Note:

Hadamard product $A \ast$

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2

New Number: 5.82 |  AESZ: 313  |  Superseeker: 45 43531  |  Hash: f8bfe82988e14680bdb775a3ce956216  

Degree: 5

\(\theta^4-x(\theta+1)(285\theta^3+321\theta^2+128\theta+18)-2 x^{2}\left(1640\theta^4+1322\theta^3-1337\theta^2-1178\theta-240\right)-2^{2} 3^{2} x^{3}\left(213\theta^4-256\theta^3-286\theta^2-80\theta-5\right)+2^{3} 3^{3} x^{4}(2\theta+1)(22\theta^3+37\theta^2+24\theta+6)+2^{4} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 18, 1662, 236340, 40943070, ...
--> OEIS
Normalized instanton numbers (n0=1): 45, 845, 43531, 3091112, 273471538, ... ; Common denominator:...

Discriminant

\((z-1)(48z^2+296z-1)(6z+1)^2\)

Local exponents

\(-\frac{ 37}{ 12}-\frac{ 7}{ 6}\sqrt{ 7}\)\(-\frac{ 1}{ 6}\)\(0\)\(-\frac{ 37}{ 12}+\frac{ 7}{ 6}\sqrt{ 7}\)\(1\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)
\(2\)\(4\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.82" from ...

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