Summary

You searched for: degz=3

Your search produced 34 matches
 1-30  31-34 

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31

New Number: 3.6 |  AESZ: ~33  |  Superseeker: 196 2993772  |  Hash: 29aeacb8c7e91c8c2838e65ce2750b5a  

Degree: 3

\(\theta^4+2^{2} x\left(60\theta^4-8\theta^3+31\theta^2+35\theta+6\right)-2^{10} x^{2}(4\theta+3)(132\theta^3+395\theta^2+363\theta+69)-2^{14} 7^{2} x^{3}(4\theta+1)(4\theta+3)(4\theta+7)(4\theta+9)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -24, 13992, -920832, 1808021160, ...
--> OEIS
Normalized instanton numbers (n0=1): 196, 17212, 2993772, 789858520, 260782261024, ... ; Common denominator:...

Discriminant

\(-(784z-1)(1+512z)^2\)

Local exponents

\(-\frac{ 1}{ 512}\)\(0\)\(\frac{ 1}{ 784}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 4}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(\frac{ 3}{ 4}\)
\(1\)\(0\)\(1\)\(\frac{ 7}{ 4}\)
\(\frac{ 3}{ 2}\)\(0\)\(2\)\(\frac{ 9}{ 4}\)

Note:

Operator AESZ 33 is replaced by this equivalent operator.

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32

New Number: 3.7 |  AESZ: ~73  |  Superseeker: 90 151648  |  Hash: 9f672e1168859bdcc8ddc7a201c57968  

Degree: 3

\(\theta^4-2 3^{2} x\left(6\theta^4+12\theta^3+3\theta^2-3\theta-1\right)-2^{2} 3^{6} x^{2}(\theta+1)^2(20\theta^2+40\theta+17)-2^{4} 3^{10} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -18, 2754, 37620, 43789410, ...
--> OEIS
Normalized instanton numbers (n0=1): 90, 2196, 151648, 14813388, 1820806056, ... ; Common denominator:...

Discriminant

\(-(324z-1)(1+108z)^2\)

Local exponents

\(-\frac{ 1}{ 108}\)\(0\)\(\frac{ 1}{ 324}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(0\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(2\)
\(1\)\(0\)\(2\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 73

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33

New Number: 3.8 |  AESZ: ~100  |  Superseeker: 5 454  |  Hash: 82a1ac6ac6fb9ab2e4d6b5d5790d1d9b  

Degree: 3

\(\theta^4+x\left(15\theta^4+30\theta^3+35\theta^2+20\theta+4\right)-2^{5} x^{2}(\theta+1)^2(66\theta^2+132\theta+53)-2^{8} 7^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -4, 132, -1120, 72100, ...
--> OEIS
Normalized instanton numbers (n0=1): 5, 42, 454, 7498, 154351, ... ; Common denominator:...

Discriminant

\(-(49z-1)(1+32z)^2\)

Local exponents

\(-\frac{ 1}{ 32}\)\(0\)\(\frac{ 1}{ 49}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(2\)
\(1\)\(0\)\(2\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to AESZ 100= $ a \ast a$

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34

New Number: 3.9 |  AESZ: ~101  |  Superseeker: 13 2650  |  Hash: a6878d847acf199583e8168a33967174  

Degree: 3

\(\theta^4-x\left(113\theta^4+226\theta^3+173\theta^2+60\theta+8\right)-2^{3} x^{2}(\theta+1)^2(119\theta^2+238\theta+92)-2^{2} 11^{2} x^{3}(\theta+1)(\theta+2)(2\theta+1)(2\theta+5)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 336, 19880, 1420720, ...
--> OEIS
Normalized instanton numbers (n0=1): 13, 128, 2650, 79400, 2921395, ... ; Common denominator:...

Discriminant

\(-(121z-1)(4z+1)^2\)

Local exponents

\(-\frac{ 1}{ 4}\)\(0\)\(\frac{ 1}{ 121}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(1\)
\(\frac{ 1}{ 2}\)\(0\)\(1\)\(2\)
\(1\)\(0\)\(2\)\(\frac{ 5}{ 2}\)

Note:

Operator equivalent to $AESZ 101=$b \ast b$.

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