### Summary

You searched for: superseeker=-9,-3145/3

Your search produced exactly one match

1

New Number: 8.21 |  AESZ: 251  |  Superseeker: -9 -3145/3  |  Hash: dd2b60d18804c72129ba319fc8b50023

Degree: 8

$\theta^4-3 x\theta(-2-11\theta-18\theta^2+27\theta^3)-2 3^{2} x^{2}\left(39\theta^4+480\theta^3+474\theta^2+276\theta+64\right)+2^{3} 3^{4} x^{3}\left(348\theta^4+1152\theta^3+1759\theta^2+1110\theta+260\right)-2^{3} 3^{5} x^{4}\left(3420\theta^4+15912\theta^3+28437\theta^2+20544\theta+5296\right)+2^{4} 3^{7} x^{5}\left(1125\theta^4+12546\theta^3+31089\theta^2+26448\theta+7480\right)+2^{5} 3^{9} x^{6}\left(1395\theta^4+3240\theta^3-3378\theta^2-7146\theta-2696\right)-2^{7} 3^{11} x^{7}\left(351\theta^4+2646\theta^3+4767\theta^2+3309\theta+800\right)-2^{7} 3^{13} x^{8}(3\theta+2)(3\theta+4)(6\theta+5)(6\theta+7)$

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Coefficients of the holomorphic solution: 1, 0, 72, -1440, 48600, ...
--> OEIS
Normalized instanton numbers (n0=1): -9, -27/4, -3145/3, -20907/4, -327348, ... ; Common denominator:...

#### Discriminant

$-(54z+1)(27z-1)(432z^2-36z+1)(-1+36z+324z^2)^2$

#### Local exponents

$-\frac{ 1}{ 18}-\frac{ 1}{ 18}\sqrt{ 2}$$-\frac{ 1}{ 54}$$0$$-\frac{ 1}{ 18}+\frac{ 1}{ 18}\sqrt{ 2}$$\frac{ 1}{ 27}$$\frac{ 1}{ 24}-\frac{ 1}{ 72}\sqrt{ 3}I$$\frac{ 1}{ 24}+\frac{ 1}{ 72}\sqrt{ 3}I$$\infty$
$0$$0$$0$$0$$0$$0$$0$$\frac{ 2}{ 3}$
$1$$1$$0$$1$$1$$1$$1$$\frac{ 5}{ 6}$
$3$$1$$0$$3$$1$$1$$1$$\frac{ 7}{ 6}$
$4$$2$$0$$4$$2$$2$$2$$\frac{ 4}{ 3}$

#### Note:

This is operator "8.21" from ...