Summary

You searched for: superseeker=10,7709/9

Your search produced 2 matches

You can download all data as plain text or as JSON

1

New Number: 10.4 |  AESZ:  |  Superseeker: 10 7709/9  |  Hash: 6162ae56594cb4ca6830174a8ed00300  

Degree: 10

\(\theta^4+x\left(14+63\theta+102\theta^2+78\theta^3+231\theta^4\right)+x^{2}\left(2832+13390\theta+24563\theta^2+19308\theta^3+21987\theta^4\right)+2^{3} x^{3}\left(140700\theta^4+225708\theta^3+290537\theta^2+177465\theta+44084\right)+2^{4} 3 x^{4}\left(713295\theta^4+1769710\theta^3+2523886\theta^2+1767335\theta+499986\right)+2^{6} x^{5}\left(10296675\theta^4+36211314\theta^3+60921650\theta^2+49433683\theta+15811528\right)+2^{6} x^{6}\left(137088291\theta^4+659829216\theta^3+1356977569\theta^2+1291863456\theta+467669756\right)+2^{9} x^{7}\left(179375706\theta^4+1143044916\theta^3+2845532295\theta^2+3114799053\theta+1242790862\right)+2^{12} x^{8}\left(184827267\theta^4+1416425484\theta^3+3980381306\theta^2+4736268700\theta+1991273435\right)+2^{16} 47 x^{9}(2\theta+3)(622034\theta^3+4130865\theta^2+8390461\theta+4891218)+2^{20} 3 17^{2} 47^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -14, 250, -5192, 116266, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...

Discriminant

\((24z+1)(2312z^3+75z^2+15z+1)(32z+1)^2(376z^2+64z+1)^2\)

Local exponents

\(-\frac{ 4}{ 47}-\frac{ 9}{ 188}\sqrt{ 2}\) ≈\(-0.055617\)\(-\frac{ 1}{ 24}\)\(-\frac{ 1}{ 32}\)\(-\frac{ 4}{ 47}+\frac{ 9}{ 188}\sqrt{ 2}\)\(0\) ≈\(0.011589-0.087422I\) ≈\(0.011589+0.087422I\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(3\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(4\)\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(3\)

Note:

This is operator "10.4" from ...

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

2

New Number: 13.7 |  AESZ:  |  Superseeker: 10 7709/9  |  Hash: 47093f7f3b7ab4544ef6b418bdae778b  

Degree: 13

\(\theta^4+x\left(127\theta^4-2\theta^3+22\theta^2+23\theta+6\right)+x^{2}\left(4803\theta^4+1644\theta^3+3459\theta^2+430\theta-384\right)+2^{3} x^{3}\left(2507\theta^4+8118\theta^3-2448\theta^2-7127\theta-2940\right)-2^{4} x^{4}\left(94175\theta^4+88358\theta^3+133418\theta^2+111507\theta+38898\right)+2^{6} 3 x^{5}\left(22347\theta^4+197706\theta^3+783766\theta^2+893091\theta+359952\right)+2^{6} 3^{2} x^{6}\left(869067\theta^4+4718208\theta^3+11162457\theta^2+11758320\theta+4583500\right)-2^{9} 3^{3} x^{7}\left(245985\theta^4+1338174\theta^3+3414812\theta^2+4418167\theta+2103502\right)-2^{12} 3^{4} x^{8}\left(234234\theta^4+2167368\theta^3+7012373\theta^2+9416514\theta+4375751\right)+2^{15} 3^{5} x^{9}\left(81234\theta^4+643380\theta^3+1815861\theta^2+2193249\theta+947968\right)+2^{18} 3^{6} x^{10}(\theta+1)(15879\theta^3+214401\theta^2+816191\theta+896789)-2^{21} 3^{7} x^{11}(\theta+1)(\theta+2)(8037\theta^2+71103\theta+151546)+2^{27} 3^{9} x^{12}(\theta+3)(\theta+2)(\theta+1)(31\theta+152)-2^{29} 3^{9} 5 x^{13}(\theta+1)(\theta+2)(\theta+3)(\theta+4)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -6, 90, -1368, 21546, ...
--> OEIS
Normalized instanton numbers (n0=1): 10, -149/2, 7709/9, -27333/2, 242829, ... ; Common denominator:...

Discriminant

\(-(16z+1)(2160z^3+27z^2-9z+1)(24z+1)^2(72z^2-48z-1)^2(8z-1)^3\)

Local exponents

≈\(-0.100198\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 24}\)\(\frac{ 1}{ 3}-\frac{ 1}{ 4}\sqrt{ 2}\)\(0\) ≈\(0.043849-0.05194I\) ≈\(0.043849+0.05194I\)\(\frac{ 1}{ 8}\)\(\frac{ 1}{ 3}+\frac{ 1}{ 4}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(2\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(\frac{ 3}{ 2}\)\(3\)\(3\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(2\)\(4\)\(4\)

Note:

This is operator "13.7" from ...

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