Version 1
: Received: 1 August 2020 / Approved: 3 August 2020 / Online: 3 August 2020 (00:28:39 CEST)
How to cite:
Khan, W.A.; Khan, A.; Duran, U. A Note on Type 2 Degenerate Multi-Poly-Bernoulli Polynomials and Numbers. Preprints2020, 2020080057. https://doi.org/10.20944/preprints202008.0057.v1
Khan, W.A.; Khan, A.; Duran, U. A Note on Type 2 Degenerate Multi-Poly-Bernoulli Polynomials and Numbers. Preprints 2020, 2020080057. https://doi.org/10.20944/preprints202008.0057.v1
Khan, W.A.; Khan, A.; Duran, U. A Note on Type 2 Degenerate Multi-Poly-Bernoulli Polynomials and Numbers. Preprints2020, 2020080057. https://doi.org/10.20944/preprints202008.0057.v1
APA Style
Khan, W.A., Khan, A., & Duran, U. (2020). A Note on Type 2 Degenerate Multi-Poly-Bernoulli Polynomials and Numbers. Preprints. https://doi.org/10.20944/preprints202008.0057.v1
Chicago/Turabian Style
Khan, W.A., Aysha Khan and Ugur Duran. 2020 "A Note on Type 2 Degenerate Multi-Poly-Bernoulli Polynomials and Numbers" Preprints. https://doi.org/10.20944/preprints202008.0057.v1
Abstract
Inspired by the definition of degenerate multi-poly-Genocchi polynomials given by using the degenerate multi-polyexponential functions. In this paper, we consider a class of new generating function for the degenerate multi-poly-Bernoulli polynomials, called the type 2 degenerate multi-poly-Bernoulli polynomials by means of the degenerate multiple polyexponential functions. Then, we investigate their some properties and relations. We show that the type 2 degenerate multi-poly-Bernoulli polynomials equals a linear combination of the weighted degenerate Bernoulli polynomials and Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Bernoulli numbers and degenerate Whitney numbers.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
