Summary

You searched for: inst=-8

Your search produced 3 matches

You can download all data as plain text or as JSON

1

New Number: 2.57 |  AESZ: 184  |  Superseeker: 2 -8  |  Hash: ee8bb517b329e58eeb4352dc3cdc3f81  

Degree: 2

\(\theta^4-2 x(2\theta+1)^2(11\theta^2+11\theta+5)+2^{2} 5^{3} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 210, 5500, 159250, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, 4, -8, -194, -2820, ... ; Common denominator:...

Discriminant

\(1-88z+2000z^2\)

Local exponents

\(0\)\(\frac{ 11}{ 500}-\frac{ 1}{ 250}I\)\(\frac{ 11}{ 500}+\frac{ 1}{ 250}I\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \eta$

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

2

New Number: 6.2 |  AESZ:  |  Superseeker: -8 -1552/3  |  Hash: fd7b14f2d0f2a78723588771a9b1a984  

Degree: 6

\(\theta^4-x\left(280\theta^4+560\theta^3+686\theta^2+406\theta+93\right)+3 x^{2}\left(9296\theta^4+37184\theta^3+66322\theta^2+58276\theta+20863\right)-2 x^{3}\left(594560\theta^4+3567360\theta^3+8664912\theta^2+9941616\theta+4484205\right)+x^{4}\left(21204736\theta^4+169637888\theta^3+520783424\theta^2+726030592\theta+387696585\right)-2^{3} 3^{2} 5^{2} x^{5}(4\theta+9)(4\theta+11)(4144\theta^2+20720\theta+28335)+2^{4} 3^{4} 5^{4} x^{6}(4\theta+9)(4\theta+11)(4\theta+13)(4\theta+15)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 93, 15717/2, 1345795/2, 473123715/8, ...
--> OEIS
Normalized instanton numbers (n0=1): -8, -44, -1552/3, -8044, -138528, ... ; Common denominator:...

Discriminant

\((100z-1)^2(4z-1)^2(36z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 100}\)\(\frac{ 1}{ 36}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 9}{ 4}\)
\(0\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(-\frac{ 1}{ 2}\)\(\frac{ 11}{ 4}\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 13}{ 4}\)
\(0\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 3}{ 2}\)\(\frac{ 15}{ 4}\)

Note:

This is operator "6.2" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex  

3

New Number: 7.11 |  AESZ:  |  Superseeker: -8 -3784/3  |  Hash: cb1bf6566f9c1a0dbfe98fb55f81944c  

Degree: 7

\(\theta^4+2^{2} x\left(23\theta^4-34\theta^3-30\theta^2-13\theta-2\right)+2^{5} x^{2}\left(177\theta^4+108\theta^3+577\theta^2+518\theta+116\right)+2^{10} x^{3}\left(355\theta^4+960\theta^3+1178\theta^2+139\theta-44\right)+2^{15} x^{4}\left(451\theta^4+1228\theta^3+997\theta^2+489\theta+103\right)+2^{20} x^{5}\left(285\theta^4+720\theta^3+766\theta^2+410\theta+83\right)+2^{26} x^{6}(2\theta+1)(20\theta^3+50\theta^2+49\theta+17)+2^{31} x^{7}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, -120, -4480, 55720, ...
--> OEIS
Normalized instanton numbers (n0=1): -8, 43/2, -3784/3, 51036, -1659840, ... ; Common denominator:...

Discriminant

\((8z+1)(32768z^3+3072z^2-12z+1)(32z+1)^3\)

Local exponents

\(-\frac{ 1}{ 8}\) ≈\(-0.100423\)\(-\frac{ 1}{ 32}\)\(0\) ≈\(0.003336-0.01711I\) ≈\(0.003336+0.01711I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(1\)\(2\)\(0\)\(1\)\(1\)\(1\)
\(1\)\(1\)\(3\)\(0\)\(1\)\(1\)\(1\)
\(2\)\(2\)\(5\)\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

This is operator "7.11" from ...

Show more...  or download as   plain text  |  PDF  |  Maple  |  LaTex