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Theory and Modern Applications

Table 10 Approximate solutions of \({}_{L}e_{n}(x,y)\)

From: Certain results on a hybrid class of the Boas–Buck polynomials

Degree n

Real roots

Complex roots

1

6.0

2

7 − 3.6055 i, 7 + 3.6055 i

3

11.0158

6.4921 − 6.5438 i, 6.4921 + 6.5438 i

4

5.4531 − 9.1917 i, 5.4531 + 9.1917 i,

12.5469 − 2.5837 i, 12.5469 + 2.5837 i

5

16.5244

4.1237 − 11.5904 i, 4.1237 + 11.5904 i,

12.6141 − 5.3208 i, 12.6141 + 5.3208 i

6

2.5968 − 13.7943 i, 2.5968 + 13.7943 i,

12.3359 − 8.0810 i, 12.3359 + 8.0810 i,

18.0672 − 1.3250 i, 18.0672 + 1.3250 i

7

22.6802

0.9244 − 15.8430 i, 0.9244 + 15.8430 i,

11.7720 − 10.6952 i, 11.7720 + 10.6952 i,

17.9634 − 4.2342 i, 17.9634 + 4.2342 i

8

21.9201, 25.7017

−0.8611 − 17.7645 i, −0.8611 + 17.7645 i,

10.9879 − 13.1768 i, 10.9879 + 13.1768 i,

18.0622 − 7.0034 i, 18.0622 + 7.0034 i