Abstract
Poly-Bernoulli polynomials of the second kind were introduced in Kim et al. (Adv. Differ. Equ. 2014:219, 2014) as a generalization of the Bernoulli polynomial of the second kind. Here we investigate those polynomials and derive further results about them by using umbral calculus.
Highlights
Following Kaneko [ ], the poly-Bernoulli polynomials have been studied by many researchers in recent decades
For k ∈ Z, the poly-Bernoulli polynomials b(nk)(x) of the second kind are given by the generating function
The aim of the present paper is to present several new identities for the poly-Bernoulli polynomials by the use of umbral calculus
Summary
Following Kaneko [ ], the poly-Bernoulli polynomials have been studied by many researchers in recent decades. For k ∈ Z, the poly-Bernoulli polynomials b(nk)(x) of the second kind are given by the generating function When x = , b(nk) = b(nk)( ) are called the poly-Bernoulli numbers of the second kind.
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