### Summary

You searched for: inst=-36

1

New Number: 2.36 |  AESZ:  |  Superseeker: -36 128217204  |  Hash: 4dbde07f1392f8d49d0e10858d3a17f1

Degree: 2

$\theta^4-2^{2} 3^{2} x(3\theta+1)(3\theta+2)(72\theta^2+72\theta+31)+2^{8} 3^{8} x^{2}(3\theta+1)(3\theta+2)(3\theta+4)(3\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 2232, 13377960, 102324983040, 875961004703400, ...
--> OEIS
Normalized instanton numbers (n0=1): -36, -486279, 128217204, -74772628524, 63925611915744, ... ; Common denominator:...

#### Discriminant

$(11664z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 11664}$$\infty$
$0$$0$$\frac{ 1}{ 3}$
$0$$\frac{ 1}{ 6}$$\frac{ 2}{ 3}$
$0$$\frac{ 5}{ 6}$$\frac{ 4}{ 3}$
$0$$1$$\frac{ 5}{ 3}$

#### Note:

This is operator "2.36" from ...

2

New Number: 4.5 |  AESZ:  |  Superseeker: -36 -62596/3  |  Hash: f5b4785eb6dd46eea771050179115d33

Degree: 4

$\theta^4-2^{2} 3 x\left(48\theta^4+96\theta^3+115\theta^2+67\theta+15\right)+2^{4} 3^{2} x^{2}\left(480\theta^4+1920\theta^3+2580\theta^2+1320\theta+151\right)+2^{8} 3^{4} x^{3}(48\theta^2+144\theta+145)(2\theta+3)^2+2^{14} 3^{6} x^{4}(\theta+2)^2(2\theta+3)(2\theta+5)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 180, 44676, 11798640, 3241596996, ...
--> OEIS
Normalized instanton numbers (n0=1): -36, -756, -62596/3, -839088, -37432800, ... ; Common denominator:...

#### Discriminant

$(-1+288z+6912z^2)^2$

#### Local exponents

$-\frac{ 1}{ 48}-\frac{ 1}{ 72}\sqrt{ 3}$$0$$s_1$$s_2$$-\frac{ 1}{ 48}+\frac{ 1}{ 72}\sqrt{ 3}$$\infty$
$0$$0$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$0$$\frac{ 3}{ 2}$
$-\frac{ 1}{ 2}$$0$$0$$0$$-\frac{ 1}{ 2}$$2$
$1$$0$$1$$1$$1$$2$
$\frac{ 3}{ 2}$$0$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 5}{ 2}$

#### Note:

YY-Operator equivalent to $d \ast e \tilde A\st \epsilon$