Summary

You searched for: superseeker=10,3394/3

1

New Number: 7.20 |  AESZ:  |  Superseeker: 10 3394/3  |  Hash: 9d5791eaabb9d0e9cb4b5cd0b2158b12

Degree: 7

$\theta^4-x\left(88\theta^3-4+71\theta^4+42\theta^2-2\theta\right)-x^{2}\left(10462\theta+13294\theta^2+875\theta^4+6848\theta^3+3132\right)+3^{2} x^{3}\left(373\theta^4-6360\theta^3-30716\theta^2-44868\theta-23180\right)+3^{4} x^{4}\left(1843\theta^4+8384\theta^3+3236\theta^2-14996\theta-15180\right)+3^{8} x^{5}\left(75\theta^4+1272\theta^3+3454\theta^2+3554\theta+1192\right)-3^{11} x^{6}\left(27\theta^4-414\theta^2-918\theta-584\right)-3^{16} x^{7}\left((\theta+2)^4\right)$

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Coefficients of the holomorphic solution: 1, -4, 147, 4496, 223111, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 77, 3394/3, 24029, 640402, ... ; Common denominator:...

Discriminant

$-(-1+81z)(9z-1)^2(81z^2+14z+1)^2$

Local exponents

$-\frac{ 7}{ 81}-\frac{ 4}{ 81}\sqrt{ 2}I$$-\frac{ 7}{ 81}+\frac{ 4}{ 81}\sqrt{ 2}I$$0$$\frac{ 1}{ 81}$$\frac{ 1}{ 9}$$\infty$
$0$$0$$0$$0$$0$$2$
$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$0$$1$$1$$2$
$1$$1$$0$$1$$3$$2$
$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$0$$2$$4$$2$

Note:

This is operator "7.20" from ...

2

New Number: 9.3 |  AESZ:  |  Superseeker: 10 3394/3  |  Hash: 40e3715abcc5c4cb07e700ca79f80abf

Degree: 9

$\theta^4-x\left(57\theta^4+116\theta^3+84\theta^2+26\theta+3\right)-2 x^{2}\left(894\theta^4+3208\theta^3+4571\theta^2+2771\theta+651\right)-2 x^{3}\left(7322\theta^4+56368\theta^3+124783\theta^2+101099\theta+29757\right)+2 3^{2} x^{4}\left(6967\theta^4-27080\theta^3-139991\theta^2-138507\theta-45297\right)+2 3^{4} x^{5}\left(17617\theta^4+49068\theta^3-31255\theta^2-79893\theta-34578\right)+2 3^{8} x^{6}\left(1082\theta^4+8360\theta^3+7967\theta^2+1439\theta-773\right)-2 3^{11} x^{7}\left(198\theta^4-864\theta^3-1545\theta^2-909\theta-155\right)-3^{15} x^{8}\left(69\theta^4+144\theta^3+126\theta^2+54\theta+10\right)-3^{20} x^{9}\left((\theta+1)^4\right)$

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Coefficients of the holomorphic solution: 1, 3, 135, 5349, 258039, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, 77, 3394/3, 24029, 640402, ... ; Common denominator:...

Discriminant

$-(-1+81z)(-1+9z)^2(81z^2+14z+1)^3$

Local exponents

$-\frac{ 7}{ 81}-\frac{ 4}{ 81}\sqrt{ 2}I$$-\frac{ 7}{ 81}+\frac{ 4}{ 81}\sqrt{ 2}I$$0$$\frac{ 1}{ 81}$$\frac{ 1}{ 9}$$\infty$
$0$$0$$0$$0$$0$$1$
$\frac{ 1}{ 2}$$\frac{ 1}{ 2}$$0$$1$$1$$1$
$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$0$$1$$3$$1$
$2$$2$$0$$2$$4$$1$

Note:

This is operator "9.3" from ...