Summary

You searched for: Spectrum0=0,-1/6,1,7/6

Your search produced 3 matches

You can download all data as plain text or as JSON

1

New Number: 2.59 |  AESZ: 47  |  Superseeker: -384 -164736  |  Hash: 792da990d2d2e5263bb789ad37b00d44  

Degree: 2

\(\theta^4-2^{4} 3 x(2\theta+1)^2(18\theta^2+18\theta+13)+2^{10} 3^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 624, 685584, 883925760, 1229988226320, ...
--> OEIS
Normalized instanton numbers (n0=1): -384, -1356, -164736, 96211836, -3267254400, ... ; Common denominator:...

Discriminant

\((1728z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(-\frac{ 1}{ 6}\)\(1\)
\(0\)\(1\)\(1\)
\(0\)\(\frac{ 7}{ 6}\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \kappa$

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

2

New Number: 5.64 |  AESZ: 272  |  Superseeker: 468/5 11885484  |  Hash: 467bb784f4bd6e978748e98f6ea4a573  

Degree: 5

\(5^{2} \theta^4-2^{2} 3 5 x\left(1332\theta^4+3528\theta^3+3289\theta^2+1525\theta+285\right)+2^{4} 3^{2} x^{2}\left(331776\theta^4+2602368\theta^3+4533336\theta^2+2996640\theta+724415\right)+2^{8} 3^{5} x^{3}\left(539136\theta^4+622080\theta^3-3024864\theta^2-4008960\theta-1315985\right)-2^{15} 3^{8} x^{4}\left(41472\theta^4+393984\theta^3+735984\theta^2+510912\theta+120811\right)-2^{20} 3^{11} x^{5}(12\theta+7)(12\theta+11)(12\theta+13)(12\theta+17)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 684, 761004, 985011120, 1373164693740, ...
--> OEIS
Normalized instanton numbers (n0=1): 468/5, -315477/5, 11885484, -14354122356/5, 808514230608, ... ; Common denominator:...

Discriminant

\(-(-1+432z)(1728z+5)^2(1728z-1)^2\)

Local exponents

\(-\frac{ 5}{ 1728}\)\(0\)\(\frac{ 1}{ 1728}\)\(\frac{ 1}{ 432}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 12}\)
\(1\)\(0\)\(-\frac{ 1}{ 6}\)\(1\)\(\frac{ 11}{ 12}\)
\(3\)\(0\)\(1\)\(1\)\(\frac{ 13}{ 12}\)
\(4\)\(0\)\(\frac{ 7}{ 6}\)\(2\)\(\frac{ 17}{ 12}\)

Note:

This is operator "5.64" from ...

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

3

New Number: 8.76 |  AESZ:  |  Superseeker: -204 66054580/3  |  Hash: a1b606169a188129e64002b152d24330  

Degree: 8

\(\theta^4+2^{2} 3 x\left(444\theta^4+744\theta^3+697\theta^2+325\theta+62\right)+2^{7} 3^{2} x^{2}\left(10116\theta^4+27720\theta^3+38031\theta^2+24393\theta+5891\right)+2^{12} 3^{4} x^{3}\left(45468\theta^4+131544\theta^3+190749\theta^2+142371\theta+37390\right)+2^{17} 3^{6} x^{4}\left(148068\theta^4+401112\theta^3+412641\theta^2+216243\theta+39599\right)+2^{23} 3^{9} x^{5}\left(58320\theta^4+161352\theta^3+168390\theta^2+50175\theta-1409\right)+2^{29} 3^{12} x^{6}\left(16200\theta^4+40824\theta^3+53397\theta^2+29754\theta+6131\right)+2^{35} 3^{17} x^{7}\left(360\theta^4+936\theta^3+1038\theta^2+558\theta+119\right)+2^{43} 3^{20} x^{8}(\theta+1)^2(3\theta+2)(3\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -744, 843624, -1099121280, 1536242069160, ...
--> OEIS
Normalized instanton numbers (n0=1): -204, 6654, 66054580/3, 6573546582, 118182295200, ... ; Common denominator:...

Discriminant

\((432z+1)(864z+1)(1728z+1)^2(497664z^2+288z+1)^2\)

Local exponents

\(-\frac{ 1}{ 432}\)\(-\frac{ 1}{ 864}\)\(-\frac{ 1}{ 1728}\)\(-\frac{ 1}{ 3456}-\frac{ 1}{ 3456}\sqrt{ 23}I\)\(-\frac{ 1}{ 3456}+\frac{ 1}{ 3456}\sqrt{ 23}I\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 2}{ 3}\)
\(1\)\(1\)\(-\frac{ 1}{ 6}\)\(1\)\(1\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(3\)\(3\)\(0\)\(1\)
\(2\)\(2\)\(\frac{ 7}{ 6}\)\(4\)\(4\)\(0\)\(\frac{ 4}{ 3}\)

Note:

This is operator "8.76" from ...

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