A numerical investigation of the structure of the roots of \(q\)-Bernoulli polynomials
The author studies the \(q\)-Bernoulli polynomials \(B_{n,q^r}(x)\) introduced by \textit{T. Kim} [Russ. J. Math. Phys. 11, No. 1, 71--76 (2004; Zbl 1115.11068)]. Some identities for them are given including the reflection symmetry \[ B_{n,q^{-r}}(1-x)=(-1)^nq^{rn-r}B_{n,q^r}(x),\quad n\geq 0. \] Zeros of some of these polynomials are calculated numerically, which leads the author to a conjecture about the location of the zeros.
scientific article; zbMATH DE number 5140488
scientific article