### Summary

You searched for: superseeker=-32/5,-863/5

Your search produced exactly one match

1

New Number: 8.61 |  AESZ:  |  Superseeker: -32/5 -863/5  |  Hash: 9699709447380eb1373469a1cf5a9586

Degree: 8

$5^{2} \theta^4+5 x\left(351\theta^4+894\theta^3+752\theta^2+305\theta+50\right)+x^{2}\left(17519\theta^4+143132\theta^3+257359\theta^2+171910\theta+41600\right)-2^{3} x^{3}\left(29420\theta^4+38388\theta^3-153289\theta^2-215145\theta-74900\right)-2^{4} 3 x^{4}\left(21007\theta^4+218446\theta^3+428718\theta^2+312263\theta+79010\right)+2^{6} x^{5}\left(140935\theta^4+605458\theta^3+887488\theta^2+551709\theta+125368\right)-2^{6} x^{6}\left(70937\theta^4+221280\theta^3+204067\theta^2+54336\theta-3916\right)+2^{9} x^{7}\left(1182\theta^4+2556\theta^3+2095\theta^2+817\theta+142\right)-2^{12} x^{8}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, -10, 190, -4888, 151246, ...
--> OEIS
Normalized instanton numbers (n0=1): -32/5, -33/10, -863/5, 715/2, -83882/5, ... ; Common denominator:...

#### Discriminant

$-(8z+1)(8z^3-1119z^2-75z-1)(5-32z+8z^2)^2$

#### Local exponents

$-\frac{ 1}{ 8}$ ≈$-0.048631$ ≈$-0.018367$$0$$2-\frac{ 3}{ 4}\sqrt{ 6}$$2+\frac{ 3}{ 4}\sqrt{ 6}$ ≈$139.941998$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$0$$1$$1$$1$$1$
$1$$1$$1$$0$$3$$3$$1$$1$
$2$$2$$2$$0$$4$$4$$2$$1$

#### Note:

This is operator "8.61" from ...