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Table 11 Approximate solutions of \({}_{\mathcal{H}^{(r)}}\mathit{F}^{(c,\upsilon )}_{n}(x,y,z)\)

From: Construction of a new family of Fubini-type polynomials and its applications

Degree n Real roots Complex roots
1 −8.0
2 −9.7321, −6.2679
3 −12.4486 −5.7757 − 2.4171i, −5.7757 + 2.4171i
4 −15.7331, −3.2498 −6.5085 − 5.0405i, −6.5085 + 5.0405i
5 −18.8334, −8.0471, −0.4824 −6.3186 − 7.73086i, −6.3186 + 7.73086i
6 −21.9822, 2.4281 −8.4121 − 3.3098i, −8.4121 + 3.3098i,
−5.8108 − 10.0564i, −5.81082 + 10.0564i
7 −25.1389, −9.3486, 5.3876 −8.2941 − 5.9519i, −8.2941 + 5.9519i,
−5.1559 − 12.1304i, −5.1559 + 12.1304i