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A NOTE ON DEGENERATE MULTI-POLY-BERNOULLI POLYNOMIALS

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Recently, Kim-Kim-Kim-Kwon considered the degenerate multi-poly-Genocchi poly- nomials which are de ned by the degenerate multiple polyexponential functions. Motivated from their work, we consider the degenerate multi-poly-Bernoulli polynomials and investigate some properties of those polynomials. Also, Kim introduced the degenerate multiple polylogarithm functions which are multiple version of the degenerate modi ed polylogarithm function. We also consider the degenerate type 2 multi-poly-Bernoulli polynomials which are explained by those functions. These are extensions of the degenerate type 2 poly-Bernoulli polynomials which are investigated by Kim-Kim-Kwon-Lee. We obtain explicit expressions and some properties for the degenerate type 2 multi-poly-Bernoulli polynomials

Abstract

Recently, Kim-Kim-Kim-Kwon considered the degenerate multi-poly-Genocchi poly- nomials which are de ned by the degenerate multiple polyexponential functions. Motivated from their work, we consider the degenerate multi-poly-Bernoulli polynomials and investigate some properties of those polynomials. Also, Kim introduced the degenerate multiple polylogarithm functions which are multiple version of the degenerate modi ed polylogarithm function. We also consider the degenerate type 2 multi-poly-Bernoulli polynomials which are explained by those functions. These are extensions of the degenerate type 2 poly-Bernoulli polynomials which are investigated by Kim-Kim-Kwon-Lee. We obtain explicit expressions and some properties for the degenerate type 2 multi-poly-Bernoulli polynomials

참고문헌 (20)

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  4. L.-C. Jang, "A note on degenerate type 2 multi-poly-Genocchi polynomials", ~
  5. W. A. Khan, "A Note on Type 2 Degenerate Multi-Poly-Bernoulli Polyno-mials and Numbers", Preprints 2020, 2020080057, ~ (2020)
  6. D. S. Kim, "A note on polyexponential and unipoly functions", Russ. J. Math. Phys, 26(1), pp.40~49 (2019)
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  8. D. S. Kim, "A note on degenerate poly-Bernoulli numbers and polynomials", Adv. Difference Equ, pp.258~ (2015)
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  10. 김택연, "A note on degenerate stirling polynomials of the second kind", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(3), pp.319~332 (2017), 장전수학회[DOI]
  11. T. Kim, "Degenerate polyexponential functions and degenerate Bell polynomials", J. Math. Anal. Appl, 487(2), pp.124017~ (2020)
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  13. 김태균, "A NOTE ON DEGENERATE MULTI-POLY-GENOCCHI POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 30(3), pp.447~454 (2020), 장전수학회
  14. T. Kim, "Degenerate poly-Bernoulli polynomials arising from degenerate polylogarithm", Adv. Difference Equ, pp.444~ (2020)
  15. T. Kim, "A note on degenerate Genocchi and polyGenocchi numbers and polynomials", J. Inequal. Appl, pp.110~ (2020)
  16. T. Kim, "Degenerate polyexponential functions and type 2 degen-erate poly-Bernoulli numbers and polynomials", Adv. Difference Equ, pp.168~ (2020)
  17. D. S. Lee, "Type 2 degenerate poly-Euler polynomials", Symmetry, 12(6), pp.1011~ (2020)
  18. L. Lewin, "Polylogarithms and associated functions" (1981), North-Holland Publishing Co
  19. F. Qi, "MULTIPLE-POLY-BERNOULLI POLYNOMIALS OF THE SECOND KIND", Advanced Studies in Contemporary Mathematics, 25(1), pp.1~7 (2015), 장전수학회
  20. M. Waldschmidt, "Multiple polylogarithms: an introduction", ~ (2000)

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