Summary

You searched for: sol=228

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1

New Number: 4.6 |  AESZ:  |  Superseeker: -28 1036  |  Hash: e42780ff25b428328423d5eea814a37a  

Degree: 4

\(\theta^4-2^{2} x\left(176\theta^4+352\theta^3+427\theta^2+251\theta+57\right)+2^{4} x^{2}\left(11744\theta^4+46976\theta^3+84756\theta^2+75560\theta+27275\right)-2^{8} 5^{3} x^{3}(176\theta^2+528\theta+537)(2\theta+3)^2+2^{14} 5^{6} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)\)

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Coefficients of the holomorphic solution: 1, 228, 44716, 8258768, 1469227500, ...
--> OEIS
Normalized instanton numbers (n0=1): -28, -21, 1036, 53976, 1260496, ... ; Common denominator:...

Discriminant

\((1-352z+32000z^2)^2\)

Local exponents

\(0\)\(s_1\)\(s_2\)\(\frac{ 11}{ 2000}-\frac{ 1}{ 1000}I\)\(\frac{ 11}{ 2000}+\frac{ 1}{ 1000}I\)\(\infty\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(0\)\(0\)\(\frac{ 3}{ 2}\)
\(0\)\(0\)\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(2\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(2\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 5}{ 2}\)

Note:

YY-operator equivalent to AESZ 121 =$b \ast e \tilde A \ast \eta$

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2

New Number: 8.47 |  AESZ:  |  Superseeker: 31/3 43174/9  |  Hash: b79bf25fcecf028aa40c1a6a8233efe7  

Degree: 8

\(3^{4} \theta^4-3^{3} x\left(367\theta^4+398\theta^3+295\theta^2+96\theta+12\right)-2^{4} 3^{3} x^{2}\left(200\theta^4+2081\theta^3+3614\theta^2+2009\theta+392\right)+2^{6} 3 x^{3}\left(72449\theta^4+102684\theta^3-48579\theta^2-77922\theta-22536\right)+2^{10} x^{4}\left(109873\theta^4+619970\theta^3+56260\theta^2-219027\theta-78216\right)-2^{14} 7 x^{5}\left(40669\theta^4-18266\theta^3-36570\theta^2-16190\theta-1955\right)-2^{17} 7 x^{6}\left(80805\theta^4+76590\theta^3+51265\theta^2+23076\theta+4780\right)-2^{24} 7^{2} x^{7}\left(437\theta^4+1117\theta^3+1236\theta^2+664\theta+140\right)-2^{29} 3 7^{2} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)

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Coefficients of the holomorphic solution: 1, 4, 228, 12640, 901540, ...
--> OEIS
Normalized instanton numbers (n0=1): 31/3, 1964/9, 43174/9, 1469755/9, 19813517/3, ... ; Common denominator:...

Discriminant

\(-(27z+1)(2048z^3+768z^2+112z-1)(-9+168z+3584z^2)^2\)

Local exponents

≈\(-0.191715-0.145483I\) ≈\(-0.191715+0.145483I\)\(-\frac{ 3}{ 128}-\frac{ 3}{ 896}\sqrt{ 273}\)\(-\frac{ 1}{ 27}\)\(0\) ≈\(0.00843\)\(-\frac{ 3}{ 128}+\frac{ 3}{ 896}\sqrt{ 273}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(1\)\(1\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(1\)\(0\)\(1\)\(3\)\(1\)
\(2\)\(2\)\(4\)\(2\)\(0\)\(2\)\(4\)\(\frac{ 4}{ 3}\)

Note:

This is operator "8.47" from ...

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