### Summary

You searched for: inst=270

1

New Number: 2.64 |  AESZ: 182  |  Superseeker: 1 7  |  Hash: 89ba4729efa82413b33fe6928ff8d2c9

Degree: 2

$\theta^4-x\left(43\theta^4+86\theta^3+77\theta^2+34\theta+6\right)+2^{2} 3 x^{2}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 66, 924, 14850, ...
--> OEIS
Normalized instanton numbers (n0=1): 1, 7/4, 7, 40, 270, ... ; Common denominator:...

#### Discriminant

$(27z-1)(16z-1)$

#### Local exponents

$0$$\frac{ 1}{ 27}$$\frac{ 1}{ 16}$$\infty$
$0$$0$$0$$\frac{ 5}{ 6}$
$0$$1$$1$$1$
$0$$1$$1$$1$
$0$$2$$2$$\frac{ 7}{ 6}$

#### Note:

This is operator "2.64" from ...

2

New Number: 5.89 |  AESZ: 329  |  Superseeker: 48 25200  |  Hash: 8c526b3b825d5ad6a3d0fb83ee4e6059

Degree: 5

$\theta^4-2^{4} x\left(8\theta^4+34\theta^3+25\theta^2+8\theta+1\right)-2^{8} x^{2}\left(87\theta^4+150\theta^3+32\theta^2-2\theta-1\right)-2^{12} x^{3}\left(202\theta^4+240\theta^3+211\theta^2+102\theta+19\right)-2^{16} 3 x^{4}(2\theta+1)(22\theta^3+45\theta^2+38\theta+12)-2^{20} 3^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1200, 136960, 19010320, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 270, 25200, 968066, 80892688, ... ; Common denominator:...

#### Discriminant

$-(16384z^3+3072z^2+224z-1)(1+48z)^2$

#### Local exponents

≈$-0.095858-0.072741I$ ≈$-0.095858+0.072741I$$-\frac{ 1}{ 48}$$0$ ≈$0.004215$$\infty$
$0$$0$$0$$0$$0$$\frac{ 1}{ 2}$
$1$$1$$1$$0$$1$$1$
$1$$1$$3$$0$$1$$1$
$2$$2$$4$$0$$2$$\frac{ 3}{ 2}$

#### Note:

This is operator "5.89" from ...