\(q\)-poly-Bernoulli numbers and \(q\)-poly-Cauchy numbers with a parameter by Jackson's integrals (Q904164)

The author extends poly-Bernoulli polynomials to \(q\)-poly-Bernoulli polynomials \(B_{n,\rho ,q}^{(k)} (z)\) with a parameter \(\rho \) and also extends likewise poly-Cauchy polynomials to \(q\)-poly-Cauchy polynomials of the first and second kind with parameter \(\rho \). Then the author studies relations among these polynomials.