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You searched for: degz=10

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1

New Number: 10.10 |  AESZ:  |  Superseeker: 28/3 83612/81  |  Hash: 8270c1ecc701d7cbd422a656c6118587  

Degree: 10

\(3^{2} \theta^4+2^{2} 3 x\left(220\theta^4+152\theta^3+207\theta^2+131\theta+31\right)+2^{4} x^{2}\left(20608\theta^4+32896\theta^3+50132\theta^2+37496\theta+11991\right)+2^{8} x^{3}\left(89936\theta^4+243168\theta^3+429080\theta^2+391080\theta+152645\right)+2^{12} x^{4}\left(242448\theta^4+966912\theta^3+2030168\theta^2+2199488\theta+1002377\right)+2^{20} x^{5}\left(26320\theta^4+142696\theta^3+359216\theta^2+454946\theta+237357\right)+2^{23} x^{6}\left(59600\theta^4+415872\theta^3+1247376\theta^2+1826640\theta+1079063\right)+2^{28} x^{7}\left(21712\theta^4+187424\theta^3+661000\theta^2+1107048\theta+733353\right)+2^{32} x^{8}\left(9744\theta^4+100992\theta^3+412312\theta^2+779936\theta+572857\right)+2^{39} x^{9}\left(304\theta^4+3696\theta^3+17208\theta^2+36300\theta+29211\right)+2^{44} x^{10}\left((2\theta+7)^4\right)\)

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Coefficients of the holomorphic solution: 1, -124/3, 1220, -872528/27, 67351172/81, ...
--> OEIS
Normalized instanton numbers (n0=1): 28/3, -695/9, 83612/81, -4447894/243, 274874464/729, ... ; Common denominator:...

Discriminant

\((1+48z+256z^2)(32z+1)^2(16z+1)^2(32z+3)^2(64z+1)^2\)

Local exponents

\(-\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(-\frac{ 3}{ 32}\)\(-\frac{ 1}{ 16}\)\(-\frac{ 1}{ 32}\)\(-\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(-\frac{ 1}{ 64}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 2}\)
\(1\)\(1\)\(0\)\(0\)\(1\)\(1\)\(0\)\(\frac{ 7}{ 2}\)
\(1\)\(-2\)\(1\)\(1\)\(1\)\(3\)\(0\)\(\frac{ 7}{ 2}\)
\(2\)\(3\)\(1\)\(1\)\(2\)\(4\)\(0\)\(\frac{ 7}{ 2}\)

Note:

This is operator "10.10" from ...

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2

New Number: 10.1 |  AESZ:  |  Superseeker: 118/91 268/13  |  Hash: 9708eba070b10afbba48d1f539423c22  

Degree: 10

\(7^{2} 13^{2} \theta^4-7 13 x\left(2221\theta^4+4604\theta^3+3940\theta^2+1638\theta+273\right)-2 x^{2}\left(275775\theta^4+850032\theta^3+1167211\theta^2+754481\theta+190918\right)+x^{3}\left(27353\theta^4-6829166\theta^2-6586125\theta-2489994\theta^3-2242968\right)-x^{4}\left(46728731\theta+12063734\theta^3+18386820+508804\theta^4+40173426\theta^2\right)+3 x^{5}\left(33450\theta^4+319414\theta^3-766536\theta^2-1551527\theta-668977\right)+x^{6}\left(2892684+47526449\theta^2+4076796\theta^4+26519901\theta+28614978\theta^3\right)-2 x^{7}\left(96271\theta^4+1136261\theta^3+4541506\theta^2+6411261\theta+2925345\right)-13 x^{8}(\theta+1)(257369\theta^3+699321\theta^2+523184\theta+25156)+2^{2} 5 13^{2} x^{9}(\theta+2)(\theta+1)(227\theta^2+762\theta+681)-2^{2} 5^{2} 13^{3} x^{10}(\theta+1)(\theta+2)^2(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 3, 29, 393, 6333, ...
--> OEIS
Normalized instanton numbers (n0=1): 118/91, 373/91, 268/13, 12732/91, 105020/91, ... ; Common denominator:...

Discriminant

\(-(-1+25z+49z^2+36z^3+199z^4-40z^5+13z^6)(-91-27z+130z^2)^2\)

Local exponents

\(\frac{ 27}{ 260}-\frac{ 1}{ 260}\sqrt{ 48049}\)\(0\)\(\frac{ 27}{ 260}+\frac{ 1}{ 260}\sqrt{ 48049}\)\(#ND+#NDI\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(0\)\(1\)\(1\)\(2\)
\(3\)\(0\)\(3\)\(1\)\(2\)
\(4\)\(0\)\(4\)\(2\)\(3\)

Note:

This is operator "10.1" from ...

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3

New Number: 10.2 |  AESZ:  |  Superseeker: 4 2252/9  |  Hash: 4a65f8c6ad1f8eaf4aa56879ebb94205  

Degree: 10

\(\theta^4+2^{2} x\left(69\theta^4+42\theta^3+45\theta^2+24\theta+5\right)+2^{4} x^{2}\left(2097\theta^4+2748\theta^3+3311\theta^2+1990\theta+489\right)+2^{8} x^{3}\left(9240\theta^4+19254\theta^3+26269\theta^2+17979\theta+5020\right)+2^{10} 3 x^{4}\left(34845\theta^4+101230\theta^3+156798\theta^2+120187\theta+36857\right)+2^{12} x^{5}\left(792225\theta^4+2972406\theta^3+5205467\theta^2+4394830\theta+1449907\right)+2^{14} x^{6}\left(4064601\theta^4+18714936\theta^3+36737137\theta^2+33711480\theta+11807867\right)+2^{18} x^{7}\left(3474333\theta^4+18927498\theta^3+41213301\theta^2+40674636\theta+14985820\right)+2^{20} x^{8}\left(7544547\theta^4+47365644\theta^3+113299226\theta^2+119329996\theta+45950951\right)+2^{24} 23 x^{9}(2\theta+3)(50786\theta^3+284985\theta^2+515497\theta+282264)+2^{28} 3 7^{2} 23^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -20, 436, -9872, 228292, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, -31, 2252/9, -11109/4, 33312, ... ; Common denominator:...

Discriminant

\((24z+1)(8z+1)(784z^2+52z+1)(32z+1)^2(736z^2+64z+1)^2\)

Local exponents

\(-\frac{ 1}{ 8}\)\(-\frac{ 1}{ 23}-\frac{ 3}{ 184}\sqrt{ 2}\)\(-\frac{ 1}{ 24}\)\(-\frac{ 13}{ 392}-\frac{ 3}{ 392}\sqrt{ 3}I\)\(-\frac{ 13}{ 392}+\frac{ 3}{ 392}\sqrt{ 3}I\)\(-\frac{ 1}{ 32}\)\(-\frac{ 1}{ 23}+\frac{ 3}{ 184}\sqrt{ 2}\)\(0\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(\frac{ 3}{ 2}\)
\(1\)\(3\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(\frac{ 5}{ 2}\)
\(2\)\(4\)\(2\)\(2\)\(2\)\(1\)\(4\)\(0\)\(3\)

Note:

This is operator "10.2" from ...

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4

New Number: 10.3 |  AESZ:  |  Superseeker: 2 421/9  |  Hash: 5219414e025733d8e128028821370b4b  

Degree: 10

\(\theta^4-x\left(321\theta^4+258\theta^3+258\theta^2+129\theta+26\right)+x^{2}\left(74028\theta^3+14112+55150\theta+89219\theta^2+46467\theta^4\right)-2^{3} x^{3}\left(499260\theta^4+1184748\theta^3+1665809\theta^2+1187841\theta+345452\right)+2^{4} 3 x^{4}\left(4702665\theta^4+14805730\theta^3+23754818\theta^2+18867201\theta+5979118\right)-2^{6} x^{5}\left(136927125\theta^4+537349854\theta^3+968406086\theta^2+839579917\theta+283906432\right)+2^{6} x^{6}\left(3697617171\theta^4+17401686816\theta^3+34821823585\theta^2+32540314464\theta+11600569724\right)-2^{9} x^{7}\left(8571324186\theta^4+47135706036\theta^3+103830096399\theta^2+103713883221\theta+38684901782\right)+2^{12} x^{8}\left(13055773347\theta^4+82367586444\theta^3+198438600506\theta^2+210671505052\theta+81797663483\right)-2^{16} 137 x^{9}(2\theta+3)(21527774\theta^3+121431015\theta^2+220937755\theta+121634574)+2^{20} 3 73^{2} 137^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 26, 730, 21320, 638506, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -3/2, 421/9, -519/2, 285, ... ; Common denominator:...

Discriminant

\((24z-1)(42632z^3-3675z^2+105z-1)(32z-1)^2(1096z^2-64z+1)^2\)

Local exponents

\(0\) ≈\(0.025716-0.003646I\) ≈\(0.025716+0.003646I\)\(\frac{ 4}{ 137}-\frac{ 3}{ 548}\sqrt{ 2}I\)\(\frac{ 4}{ 137}+\frac{ 3}{ 548}\sqrt{ 2}I\)\(\frac{ 1}{ 32}\) ≈\(0.034771\)\(\frac{ 1}{ 24}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(3\)

Note:

This is operator "10.3" from ...

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5

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 ...

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6

New Number: 10.5 |  AESZ:  |  Superseeker: 8 -830/9  |  Hash: 26cb7b62aea8fead9548cb08c510d8cc  

Degree: 10

\(\theta^4-x\left(5+36\theta+102\theta^2+132\theta^3+42\theta^4\right)+x^{2}\left(321+2500\theta+5078\theta^2+2676\theta^3-126\theta^4\right)+x^{3}\left(58511+193314\theta+255284\theta^2+165228\theta^3+36750\theta^4\right)+3 x^{4}\left(149076\theta^4+788140\theta^3+1818454\theta^2+1636604\theta+537147\right)+x^{5}\left(18978161+48287282\theta+41352784\theta^2+10485348\theta^3-282726\theta^4\right)+x^{6}\left(75240839+129474252\theta+18361102\theta^2-64936644\theta^3-20164434\theta^4\right)-x^{7}\left(192652267+790586058\theta+1080753300\theta^2+555817116\theta^3+53729334\theta^4\right)-x^{8}\left(1469856277+3396870740\theta+2385867946\theta^2+267688500\theta^3-184083363\theta^4\right)+2 5 13 x^{9}(2\theta+3)(3678542\theta^3+13483935\theta^2+14333215\theta+4727112)+2^{2} 3 5^{2} 13^{2} 73^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 5, 79, 791, -9329, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -45/2, -830/9, -5301/2, 2790, ... ; Common denominator:...

Discriminant

\((3z+1)(5329z^3+1587z^2-69z+1)(13z+1)^2(4z+1)^2(5z-1)^2\)

Local exponents

≈\(-0.337782\)\(-\frac{ 1}{ 3}\)\(-\frac{ 1}{ 4}\)\(-\frac{ 1}{ 13}\)\(0\) ≈\(0.019989-0.01249I\) ≈\(0.019989+0.01249I\)\(\frac{ 1}{ 5}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 5}{ 2}\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(3\)

Note:

This is operator "10.5" from ...

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7

New Number: 10.6 |  AESZ:  |  Superseeker: 8 2200/9  |  Hash: b5aa0abf76ddfbd280ec220a43822aa4  

Degree: 10

\(\theta^4+2^{2} x\left(21\theta^4-6\theta^3+3\theta+1\right)+2^{4} x^{2}\left(126\theta^4-96\theta^3-16\theta^2-56\theta-33\right)+2^{6} x^{3}\left(84\theta^4-336\theta^3-226\theta^2-366\theta-163\right)+2^{11} 3 x^{4}\left(39\theta^4+500\theta^3+1230\theta^2+1160\theta+407\right)+2^{12} x^{5}\left(7029\theta^4+50118\theta^3+125086\theta^2+129149\theta+48902\right)+2^{14} x^{6}\left(38550\theta^4+294456\theta^3+806428\theta^2+911232\theta+368273\right)+2^{16} x^{7}\left(77544\theta^4+708720\theta^3+2233434\theta^2+2804346\theta+1214177\right)+2^{20} x^{8}\left(9171\theta^4+117228\theta^3+467444\theta^2+684316\theta+324572\right)-2^{23} x^{9}(2\theta+3)(2114\theta^3+16713\theta^2+37111\theta+22497)+2^{26} 3 5^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 52, -688, 2500, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, -75/2, 2200/9, -8117/2, 47936, ... ; Common denominator:...

Discriminant

\((12z+1)(6400z^3+192z^2-24z+1)(16z+1)^2(32z^2-32z-1)^2\)

Local exponents

≈\(-0.090507\)\(-\frac{ 1}{ 12}\)\(-\frac{ 1}{ 16}\)\(\frac{ 1}{ 2}-\frac{ 3}{ 8}\sqrt{ 2}\)\(0\) ≈\(0.030254-0.02848I\) ≈\(0.030254+0.02848I\)\(\frac{ 1}{ 2}+\frac{ 3}{ 8}\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(1\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(0\)\(1\)\(1\)\(3\)\(\frac{ 5}{ 2}\)
\(2\)\(2\)\(1\)\(4\)\(0\)\(2\)\(2\)\(4\)\(3\)

Note:

This is operator "10.6" from ...

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8

New Number: 10.7 |  AESZ:  |  Superseeker: 4 -628/9  |  Hash: d5910f048831bb407eb8998c7c57e09f  

Degree: 10

\(\theta^4-2^{2} x\left(48\theta^4+48\theta^3+45\theta^2+21\theta+4\right)+2^{6} x^{2}\left(261\theta^4+489\theta^3+590\theta^2+364\theta+93\right)-2^{6} x^{3}\left(13530\theta^4+35628\theta^3+50795\theta^2+36813\theta+10853\right)+2^{8} 3 x^{4}\left(38616\theta^4+128020\theta^3+206502\theta^2+165712\theta+53013\right)-2^{10} x^{5}\left(685404\theta^4+2714928\theta^3+4854121\theta^2+4193537\theta+1415126\right)+2^{13} x^{6}\left(1419108\theta^4+6542898\theta^3+12841310\theta^2+11823966\theta+4167463\right)-2^{14} x^{7}\left(8117226\theta^4+43045764\theta^3+92299521\theta^2+90336771\theta+33184985\right)+2^{16} x^{8}\left(15319683\theta^4+93106380\theta^3+218052374\theta^2+226725820\theta+86734943\right)-2^{19} 5^{2} x^{9}(2\theta+3)(171838\theta^3+939735\theta^2+1668155\theta+905358)+2^{22} 3 5^{4} 17^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 292, 5728, 115012, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 5, -628/9, -2823/4, 672, ... ; Common denominator:...

Discriminant

\((12z-1)(18496z^3-2352z^2+84z-1)(16z-1)^2(400z^2-32z+1)^2\)

Local exponents

\(0\) ≈\(0.024764-0.009119I\) ≈\(0.024764+0.009119I\)\(\frac{ 1}{ 25}-\frac{ 3}{ 100}I\)\(\frac{ 1}{ 25}+\frac{ 3}{ 100}I\)\(\frac{ 1}{ 16}\) ≈\(0.077634\)\(\frac{ 1}{ 12}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(3\)

Note:

This is operator "10.7" from ...

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9

New Number: 10.8 |  AESZ:  |  Superseeker: 7 -2044/9  |  Hash: 772d055ae4c1a5d6a65a2b1f3ffa351b  

Degree: 10

\(\theta^4-x\left(147\theta^2+10+60\theta+174\theta^3+111\theta^4\right)+2^{2} x^{2}\left(1269\theta^4+3576\theta^3+4595\theta^2+2722\theta+639\right)-2^{2} x^{3}\left(28236\theta^4+92256\theta^3+135641\theta^2+100407\theta+29996\right)+2^{4} 3 x^{4}\left(34932\theta^4+117280\theta^3+166025\theta^2+128238\theta+41467\right)-2^{6} x^{5}\left(266139\theta^4+937698\theta^3+1398643\theta^2+1056533\theta+325061\right)+2^{8} x^{6}\left(478785\theta^4+1758504\theta^3+2952901\theta^2+2388960\theta+754208\right)-2^{8} x^{7}\left(2371176\theta^4+9770640\theta^3+17775969\theta^2+15468753\theta+5209610\right)+2^{10} x^{8}\left(1853604\theta^4+9368112\theta^3+18957629\theta^2+17669710\theta+6248237\right)-2^{12} 11 x^{9}(2\theta+3)(36502\theta^3+178659\theta^2+286703\theta+145866)+2^{16} 3 5^{2} 11^{2} x^{10}(\theta+1)(2\theta+5)(2\theta+3)(\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 154, 2548, 27370, ...
--> OEIS
Normalized instanton numbers (n0=1): 7, -31/4, -2044/9, -1380, -8520, ... ; Common denominator:...

Discriminant

\((3z-1)(6400z^3-2352z^2+84z-1)(4z-1)^2(88z^2-8z+1)^2\)

Local exponents

\(0\) ≈\(0.019222-0.010265I\) ≈\(0.019222+0.010265I\)\(\frac{ 1}{ 22}-\frac{ 3}{ 44}\sqrt{ 2}I\)\(\frac{ 1}{ 22}+\frac{ 3}{ 44}\sqrt{ 2}I\)\(\frac{ 1}{ 4}\) ≈\(0.329056\)\(\frac{ 1}{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 3}{ 2}\)
\(0\)\(1\)\(1\)\(3\)\(3\)\(\frac{ 1}{ 2}\)\(1\)\(1\)\(\frac{ 5}{ 2}\)
\(0\)\(2\)\(2\)\(4\)\(4\)\(1\)\(2\)\(2\)\(3\)

Note:

This is operator "10.8" from ...

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10

New Number: 10.9 |  AESZ:  |  Superseeker: 4 116  |  Hash: dbcf215f85612454543d472ffd3bffa9  

Degree: 10

\(\theta^4-2^{2} x\left(38\theta^4+70\theta^3+93\theta^2+58\theta+14\right)+2^{4} x^{2}\left(609\theta^4+2214\theta^3+4255\theta^2+4118\theta+1630\right)-2^{8} x^{3}\left(1357\theta^4+7284\theta^3+18055\theta^2+22233\theta+11143\right)+2^{10} x^{4}\left(7450\theta^4+52316\theta^3+157665\theta^2+230387\theta+134924\right)-2^{14} x^{5}\left(6580\theta^4+56446\theta^3+198857\theta^2+332342\theta+219249\right)+2^{16} x^{6}\left(15153\theta^4+151710\theta^3+606095\theta^2+1128594\theta+818733\right)-2^{20} x^{7}\left(5621\theta^4+63496\theta^3+280382\theta^2+568755\theta+444393\right)+2^{22} x^{8}\left(5152\theta^4+63904\theta^3+304853\theta^2+659693\theta+544236\right)-2^{26} 3 x^{9}\left(220\theta^4+2928\theta^3+14781\theta^2+33462\theta+28605\right)+2^{28} 3^{2} x^{10}\left((2\theta+7)^4\right)\)

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Coefficients of the holomorphic solution: 1, 56, 2192, 74112, 2319376, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 31/2, 116, 2477/2, 16876, ... ; Common denominator:...

Discriminant

\((1-48z+256z^2)(4z-1)^2(24z-1)^2(8z-1)^2(16z-1)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 32}-\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 24}\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 8}\)\(\frac{ 3}{ 32}+\frac{ 1}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(0\)\(\frac{ 7}{ 2}\)
\(0\)\(1\)\(1\)\(0\)\(0\)\(1\)\(1\)\(\frac{ 7}{ 2}\)
\(0\)\(1\)\(-2\)\(1\)\(1\)\(1\)\(3\)\(\frac{ 7}{ 2}\)
\(0\)\(2\)\(3\)\(1\)\(1\)\(2\)\(4\)\(\frac{ 7}{ 2}\)

Note:

This is operator "10.9" from ...

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