Theory and Modern Applications
Table 1 Numbers of real and complex zeros of \(\pmb{T_{n,q}^{(k)}(x) }\)
From: Some identities involving q-poly-tangent numbers and polynomials and distribution of their zeros
Degree n | k  = 3, q  = 1/2 | k  = −3, q  = −1/2 | ||
|---|---|---|---|---|
Real zeros | Complex zeros | Real zeros | Complex zeros | |
2 | 1 | 0 | 1 | 0 |
3 | 2 | 0 | 2 | 0 |
4 | 3 | 0 | 1 | 2 |
5 | 4 | 0 | 0 | 4 |
6 | 1 | 4 | 1 | 4 |
7 | 2 | 4 | 0 | 6 |
8 | 3 | 4 | 1 | 6 |
9 | 4 | 4 | 2 | 6 |
10 | 5 | 4 | 1 | 8 |
11 | 4 | 6 | 0 | 10 |
12 | 3 | 8 | 1 | 10 |