Generalized incomplete poly-Bernoulli polynomials and generalized incomplete poly-Cauchy polynomials

Abstract

By using the restricted and associated Stirling numbers of the first kind, we define the generalized restricted and associated poly-Cauchy polynomials. By using the restricted and associated Stirling numbers of the second kind, we define the generalized restricted and associated poly-Bernoulli polynomials. These polynomials are generalizations of original poly-Cauchy polynomials and original poly-Bernoulli polynomials, respectively. We also study their characteristic and combinatorial properties.