A Note on a New Type of Degenerate Bernoulli Numbers
Dae San Kim, T. Kim
Abstract
Studying degenerate versions of various special polynomials has became an active area of research and has yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of the polylogarithm function, the so-called degenerate polylogarithm function. Then we construct a new type of degenerate Bernoulli polynomial and number, the so-called degenerate poly-Bernoulli polynomial and number, by using the degenerate polylogarithm function, and derive several properties concerning the degenerate poly-Bernoulli numbers.
Topics & Concepts
Degenerate energy levelsPolylogarithmBernoulli numberBernoulli's principleMathematicsFunction (biology)PolynomialType (biology)Bernoulli polynomialsCombinatoricsPure mathematicsDiscrete mathematicsAlgebra over a fieldRiemann zeta functionPhysicsMathematical analysisQuantum mechanicsBiologyEcologyThermodynamicsArithmetic zeta functionEvolutionary biologyOrthogonal polynomialsPrime zeta functionClassical orthogonal polynomialsAdvanced Mathematical IdentitiesAnalytic Number Theory Research