A Note on the (ℎ,𝑞)-Extension of Bernoulli Numbers and Bernoulli Polynomials

Table 1

Numbers of real and complex zeros of 𝐵^{(ℎ)𝑛,𝑞}(𝑥).

degree 𝑛	ℎ=3		ℎ=5
	real zeros	complex zeros	real zeros	complex zeros
1	1	0	1	0
2	2	0	2	0
3	3	0	3	0
4	4	0	2	2
5	3	2	3	2
6	4	2	4	2
7	5	2	5	2
8	6	2	4	4
9	3	6	5	4
10	4	6	6	4
11	5	6	5	6
12	6	6	4	8