Article ID Journal Published Year Pages File Type
4672818 Indagationes Mathematicae 2016 12 Pages PDF
Abstract

We define qq-poly-Bernoulli polynomials Bn,ρ,q(k)(z) with a parameter ρρ, qq-poly-Cauchy polynomials of the first kind cn,ρ,q(k)(z) and of the second kind ĉn,ρ,q(k)(z) with a parameter ρρ by Jackson’s integrals, which generalize the previously known numbers and polynomials, including poly-Bernoulli numbers Bn(k) and the poly-Cauchy numbers of the first kind cn(k) and of the second kind ĉn(k). We investigate their properties connected with usual Stirling numbers and weighted Stirling numbers. We also give the relations between generalized poly-Bernoulli polynomials and two kinds of generalized poly-Cauchy polynomials.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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