### Summary

You searched for: sol=624

1

New Number: 2.33 |  AESZ:  |  Superseeker: -160 -539680  |  Hash: 83a66e92381baa083f87a13e02375bc9

Degree: 2

$\theta^4-2^{4} x(4\theta+1)(4\theta+3)(32\theta^2+32\theta+13)+2^{16} x^{2}(4\theta+1)(4\theta+3)(4\theta+5)(4\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 624, 1251600, 3268151040, 9627237219600, ...
--> OEIS
Normalized instanton numbers (n0=1): -160, -6920, -539680, -54568560, -6402958560, ... ; Common denominator:...

#### Discriminant

$(4096z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 4096}$$\infty$
$0$$0$$\frac{ 1}{ 4}$
$0$$\frac{ 1}{ 4}$$\frac{ 3}{ 4}$
$0$$\frac{ 3}{ 4}$$\frac{ 5}{ 4}$
$0$$1$$\frac{ 7}{ 4}$

#### Note:

This is operator "2.33" from ...

2

New Number: 2.59 |  AESZ: 47  |  Superseeker: -384 -164736  |  Hash: 792da990d2d2e5263bb789ad37b00d44

Degree: 2

$\theta^4-2^{4} 3 x(2\theta+1)^2(18\theta^2+18\theta+13)+2^{10} 3^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 624, 685584, 883925760, 1229988226320, ...
--> OEIS
Normalized instanton numbers (n0=1): -384, -1356, -164736, 96211836, -3267254400, ... ; Common denominator:...

#### Discriminant

$(1728z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 1728}$$\infty$
$0$$0$$\frac{ 1}{ 2}$
$0$$-\frac{ 1}{ 6}$$1$
$0$$1$$1$
$0$$\frac{ 7}{ 6}$$\frac{ 3}{ 2}$

#### Note:

Hadamard product $I \ast \kappa$