Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials
Taekyun Kim, Dae San Kim, Jongkyum Kwon, Hyunseok Lee
Abstract
Abstract The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli numbers and polynomials were defined by means of the polyexponential functions. In this paper, we introduce the degenerate polyexponential functions and the degenerate type 2 poly-Bernoulli numbers and polynomials, as degenerate versions of such functions and numbers and polynomials. We derive several explicit expressions and some identities for those numbers and polynomials.
Topics & Concepts
MathematicsDegenerate energy levelsBernoulli numberPolylogarithmBernoulli polynomialsType (biology)Ordinary differential equationPure mathematicsClassical orthogonal polynomialsDiscrete mathematicsCombinatoricsAlgebra over a fieldOrthogonal polynomialsMathematical analysisDifferential equationRiemann zeta functionPhysicsPrime zeta functionArithmetic zeta functionBiologyQuantum mechanicsEcologyAdvanced Mathematical IdentitiesAdvanced Combinatorial MathematicsAnalytic Number Theory Research