### Summary

You searched for: sol=480

1

New Number: 6.30 |  AESZ:  |  Superseeker: 4 436  |  Hash: bc45bbf252bff0ad05b31f8e076f64cb

Degree: 6

$\theta^4+2^{2} x(\theta^2+\theta+1)(18\theta^2+18\theta+5)+2^{4} x^{2}\left(39\theta^4+156\theta^3+337\theta^2+362\theta+135\right)-2^{6} x^{3}\left(1124\theta^4+6744\theta^3+14434\theta^2+12954\theta+4329\right)-2^{8} 3 7 x^{4}\left(445\theta^4+3560\theta^3+10034\theta^2+11656\theta+4779\right)-2^{10} 3^{2} 7^{2} x^{5}(\theta+4)(\theta+1)(62\theta^2+310\theta+345)-2^{12} 3^{4} 7^{3} x^{6}(\theta+5)(\theta+4)(\theta+2)(\theta+1)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -20, 480, -11264, 285712, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 71/2, 436, 6728, 127212, ... ; Common denominator:...

#### Discriminant

$-(-1+36z)(12z+1)^2(28z+1)^3$

#### Local exponents

$-\frac{ 1}{ 12}$$-\frac{ 1}{ 28}$$0$$\frac{ 1}{ 36}$$\infty$
$0$$0$$0$$0$$1$
$\frac{ 1}{ 2}$$0$$0$$1$$2$
$\frac{ 1}{ 2}$$-\frac{ 1}{ 4}$$0$$1$$4$
$1$$\frac{ 1}{ 4}$$0$$2$$5$

#### Note:

This is operator "6.30" from ...

2

New Number: 7.16 |  AESZ:  |  Superseeker: 22/5 68  |  Hash: 660211ce6175f36772066594bfc33cbb

Degree: 7

$5^{2} \theta^4-2 5 x\theta(15+71\theta+112\theta^2+38\theta^3)-2^{2} x^{2}\left(4364\theta^4+15872\theta^3+24679\theta^2+19360\theta+6000\right)-2^{4} 3^{2} 5 x^{3}\left(92\theta^4+224\theta^3+103\theta^2-176\theta-165\right)+2^{6} 3^{2} x^{4}\left(1228\theta^4+10496\theta^3+30154\theta^2+35736\theta+14715\right)+2^{9} 3^{4} x^{5}(\theta+1)(38\theta^3+74\theta^2-304\theta-495)-2^{10} 3^{4} x^{6}(2\theta+13)(2\theta+3)(17\theta+39)(\theta+1)-2^{12} 3^{6} x^{7}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 60, 480, 16524, ...
--> OEIS
Normalized instanton numbers (n0=1): 22/5, 8, 68, 3292/5, 38826/5, ... ; Common denominator:...

#### Discriminant

$-(-1+36z)(12z+5)^2(12z+1)^2(4z-1)^2$

#### Local exponents

$-\frac{ 5}{ 12}$$-\frac{ 1}{ 12}$$0$$\frac{ 1}{ 36}$$\frac{ 1}{ 4}$$\infty$
$0$$0$$0$$0$$0$$1$
$1$$0$$0$$1$$\frac{ 1}{ 2}$$\frac{ 3}{ 2}$
$3$$1$$0$$1$$\frac{ 1}{ 2}$$\frac{ 5}{ 2}$
$4$$1$$0$$2$$1$$3$

#### Note:

This is operator "7.16" from ...