### Summary

You searched for: inst=-54

Your search produced 2 matches

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1

New Number: 4.7 |  AESZ:  |  Superseeker: -54 -40552  |  Hash: ee8508b4e5567367ca11f74e074e8099

Degree: 4

$\theta^4-2 3 x\left(180\theta^4+360\theta^3+433\theta^2+253\theta+57\right)+2^{2} 3^{4} 11 x^{2}\left(108\theta^4+432\theta^3+741\theta^2+618\theta+209\right)-2^{5} 3^{8} x^{3}(60\theta^2+180\theta+181)(2\theta+3)^2+2^{8} 3^{10} x^{4}(2\theta+3)(2\theta+5)(6\theta+11)(6\theta+13)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 342, 117990, 42901884, 16240501782, ...
--> OEIS
Normalized instanton numbers (n0=1): -54, -864, -40552, -2192400, -123334380, ... ; Common denominator:...

#### Discriminant

$(432z-1)^2(108z-1)^2$

#### Local exponents

$0$$\frac{ 1}{ 432}$$\frac{ 1}{ 108}$$\infty$
$0$$0$$0$$\frac{ 3}{ 2}$
$0$$-\frac{ 1}{ 2}$$-\frac{ 1}{ 2}$$\frac{ 11}{ 6}$
$0$$1$$1$$\frac{ 13}{ 6}$
$0$$\frac{ 3}{ 2}$$\frac{ 3}{ 2}$$\frac{ 5}{ 2}$

#### Note:

YY-operator equivalent to (:AESZ 50), $\tilde B \ast \alpha$

2

New Number: 8.25 |  AESZ: 299  |  Superseeker: -54 -197216/3  |  Hash: c9e3907e21d64cf5564bf2d00992459e

Degree: 8

$\theta^4-2 3 x\left(144\theta^4+36\theta^3+47\theta^2+29\theta+6\right)+2^{2} 3^{2} x^{2}\left(8376\theta^4+6648\theta^3+8157\theta^2+3900\theta+724\right)-2^{4} 3^{4} x^{3}\left(42672\theta^4+68616\theta^3+81056\theta^2+44841\theta+9964\right)+2^{6} 3^{5} x^{4}\left(374028\theta^4+962040\theta^3+1262091\theta^2+794463\theta+195335\right)-2^{8} 3^{7} x^{5}\left(633840\theta^4+2243328\theta^3+3405968\theta^2+2385208\theta+629129\right)+2^{12} 3^{8} x^{6}\left(438960\theta^4+1884384\theta^3+3176664\theta^2+2380392\theta+652943\right)-2^{19} 3^{10} x^{7}\left(5760\theta^4+25128\theta^3+39548\theta^2+26606\theta+6517\right)+2^{22} 3^{11} x^{8}(6\theta+5)^2(6\theta+7)^2$

Maple   LaTex

Coefficients of the holomorphic solution: 1, 36, 1908, 116496, 7816500, ...
--> OEIS
Normalized instanton numbers (n0=1): -54, -1530, -197216/3, -3553920, -222887448, ... ; Common denominator:...

#### Discriminant

$(1-144z+6912z^2)(108z-1)^2(3456z^2-252z+1)^2$

#### Local exponents

$0$$\frac{ 7}{ 192}-\frac{ 1}{ 576}\sqrt{ 345}$$\frac{ 1}{ 108}$$\frac{ 1}{ 96}-\frac{ 1}{ 288}\sqrt{ 3}I$$\frac{ 1}{ 96}+\frac{ 1}{ 288}\sqrt{ 3}I$$\frac{ 7}{ 192}+\frac{ 1}{ 576}\sqrt{ 345}$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 5}{ 6}$
$0$$1$$\frac{ 1}{ 2}$$1$$1$$1$$\frac{ 5}{ 6}$
$0$$3$$\frac{ 1}{ 2}$$1$$1$$3$$\frac{ 7}{ 6}$
$0$$4$$1$$2$$2$$4$$\frac{ 7}{ 6}$

#### Note:

This is operator "8.25" from ...