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Abstract
In this paper, we introduce degenerate multi-poly-Bernoulli polynomials and derive some identities of these polynomials. We give some relationship between degenerate multi-poly-Bernoulli polynomials degenerate Whitney numbers and Stirling numbers of the first kind. Moreover, we define degenerate multi-poly-Bernoulli polynomials of complex variables, and then, we derive several properties and relations.
Highlights
For any λ ∈ R/f0g, degenerate version of the exponential function exλðtÞ is defined as follows exλðtÞ ≔ ð1 + λt Þx λ = ∞〠 ðxÞn,λ n=0 tn n! ð1Þ
We examine the results derived in this study [28, 29]
Let k1, k2, ⋯, kr ∈ Z and λ ∈ R, we consider the degenerate multi-poly-Bernoulli polynomials are given by r!Eik1
Summary
For any λ ∈ R/f0g (or C/f0g), degenerate version of the exponential function exλðtÞ is defined as follows (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]). The degenerate poly-Bernoulli polynomials, cf [12], are defined by. Letting x = 0 in (7), Bðnk,λÞð0Þ ≔ Bðnk,λÞ are called the type 2 degenerate poly-Bernoulli numbers. We examine the results derived in this study [28, 29]
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