### Summary

You searched for: superseeker=-4,140

Your search produced exactly one match

1

New Number: 8.42 |  AESZ:  |  Superseeker: -4 140  |  Hash: 7bc3855c04953ca11620400320722844

Degree: 8

$\theta^4+2^{2} x\left(26\theta^4+34\theta^3+29\theta^2+12\theta+2\right)+2^{4} x^{2}\left(305\theta^4+662\theta^3+781\theta^2+436\theta+94\right)+2^{8} x^{3}\left(519\theta^4+1278\theta^3+1541\theta^2+933\theta+213\right)+2^{10} x^{4}\left(2266\theta^4+4988\theta^3+3535\theta^2+633\theta-162\right)+2^{14} 3 x^{5}\left(569\theta^4+1184\theta^3+740\theta^2-81\theta-128\right)+2^{18} 3 x^{6}\left(254\theta^4+354\theta^3+161\theta^2-33\theta-28\right)+2^{22} 3^{2} x^{7}\left(23\theta^4+34\theta^3+8\theta^2-9\theta-4\right)-2^{27} 3^{2} x^{8}\left((\theta+1)^4\right)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -8, 112, -1664, 23056, ...
--> OEIS
Normalized instanton numbers (n0=1): -4, 1/2, 140, 1025/2, -9196, ... ; Common denominator:...

#### Discriminant

$-(32z+1)(1024z^3-896z^2-48z-1)(1+12z+192z^2)^2$

#### Local exponents

$-\frac{ 1}{ 32}-\frac{ 1}{ 96}\sqrt{ 39}I$$-\frac{ 1}{ 32}$$-\frac{ 1}{ 32}+\frac{ 1}{ 96}\sqrt{ 39}I$ ≈$-0.025859-0.019623I$ ≈$-0.025859+0.019623I$$0$ ≈$0.926719$$\infty$
$0$$0$$0$$0$$0$$0$$0$$1$
$1$$1$$1$$1$$1$$0$$1$$1$
$3$$1$$3$$1$$1$$0$$1$$1$
$4$$2$$4$$2$$2$$0$$2$$1$

#### Note:

This is operator "8.42" from ...