### Summary

You searched for: inst=66054580/3

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1

New Number: 8.76 |  AESZ:  |  Superseeker: -204 66054580/3  |  Hash: a1b606169a188129e64002b152d24330

Degree: 8

$\theta^4+2^{2} 3 x\left(444\theta^4+744\theta^3+697\theta^2+325\theta+62\right)+2^{7} 3^{2} x^{2}\left(10116\theta^4+27720\theta^3+38031\theta^2+24393\theta+5891\right)+2^{12} 3^{4} x^{3}\left(45468\theta^4+131544\theta^3+190749\theta^2+142371\theta+37390\right)+2^{17} 3^{6} x^{4}\left(148068\theta^4+401112\theta^3+412641\theta^2+216243\theta+39599\right)+2^{23} 3^{9} x^{5}\left(58320\theta^4+161352\theta^3+168390\theta^2+50175\theta-1409\right)+2^{29} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53397\theta^2+29754\theta+6131\right)+2^{35} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1038\theta^2+558\theta+119\right)+2^{43} 3^{20} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -744, 843624, -1099121280, 1536242069160, ...
--> OEIS
Normalized instanton numbers (n0=1): -204, 6654, 66054580/3, 6573546582, 118182295200, ... ; Common denominator:...

#### Discriminant

$(432z+1)(864z+1)(1728z+1)^2(497664z^2+288z+1)^2$

#### Local exponents

$-\frac{ 1}{ 432}$$-\frac{ 1}{ 864}$$-\frac{ 1}{ 1728}$$-\frac{ 1}{ 3456}-\frac{ 1}{ 3456}\sqrt{ 23}I$$-\frac{ 1}{ 3456}+\frac{ 1}{ 3456}\sqrt{ 23}I$$0$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 2}{ 3}$
$1$$1$$-\frac{ 1}{ 6}$$1$$1$$0$$1$
$1$$1$$1$$3$$3$$0$$1$
$2$$2$$\frac{ 7}{ 6}$$4$$4$$0$$\frac{ 4}{ 3}$

#### Note:

This is operator "8.76" from ...