### Summary

You searched for: sol=2682

Your search produced exactly one match

1

New Number: 8.71 |  AESZ:  |  Superseeker: -15 14044/3  |  Hash: de469dbb89801caa07ec523e3b0e4772

Degree: 8

$\theta^4+3 x\left(111\theta^4+186\theta^3+169\theta^2+76\theta+14\right)+2 3^{2} x^{2}\left(2529\theta^4+6930\theta^3+9483\theta^2+6096\theta+1508\right)+2^{2} 3^{4} x^{3}\left(11367\theta^4+32886\theta^3+47658\theta^2+36099\theta+10084\right)+2^{3} 3^{6} x^{4}\left(37017\theta^4+100278\theta^3+103626\theta^2+56025\theta+11582\right)+2^{4} 3^{9} x^{5}\left(29160\theta^4+80676\theta^3+84897\theta^2+27261\theta-568\right)+2^{5} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53991\theta^2+31131\theta+6578\right)+2^{7} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1056\theta^2+585\theta+131\right)+2^{9} 3^{20} x^{8}(\theta+1)^2(6\theta+5)(6\theta+7)$

Maple   LaTex

Coefficients of the holomorphic solution: 1, -42, 2682, -200436, 16310250, ...
--> OEIS
Normalized instanton numbers (n0=1): -15, 39, 14044/3, 213069/2, 462576, ... ; Common denominator:...

#### Discriminant

$(27z+1)(54z+1)(108z+1)^2(1944z^2+18z+1)^2$

#### Local exponents

$-\frac{ 1}{ 27}$$-\frac{ 1}{ 54}$$-\frac{ 1}{ 108}$$-\frac{ 1}{ 216}-\frac{ 1}{ 216}\sqrt{ 23}I$$-\frac{ 1}{ 216}+\frac{ 1}{ 216}\sqrt{ 23}I$$0$$\infty$
$0$$0$$0$$0$$0$$0$$\frac{ 5}{ 6}$
$1$$1$$\frac{ 1}{ 6}$$1$$1$$0$$1$
$1$$1$$\frac{ 5}{ 6}$$3$$3$$0$$1$
$2$$2$$1$$4$$4$$0$$\frac{ 7}{ 6}$

#### Note:

This is operator "8.71" from ...