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SOME IDENTITIES INVOLVING DEGENERATE r-STIRLING NUMBERS

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Recently, Kim-Kim studied the unsigned degenerate r-Stirling number of the first kind and the degenerate r-Stirling number of the second kind, respectively of which are the degenerate versions of the unsigned r-Stirling numbers of the first kind and those of the r-Stirling numbers of the second kind. The aim of this paper is to derive some identities involving such special numbers from the inverse relations for them.

Abstract

Recently, Kim-Kim studied the unsigned degenerate r-Stirling number of the first kind and the degenerate r-Stirling number of the second kind, respectively of which are the degenerate versions of the unsigned r-Stirling numbers of the first kind and those of the r-Stirling numbers of the second kind. The aim of this paper is to derive some identities involving such special numbers from the inverse relations for them.

참고문헌 (13)

  1. SERKAN ARACI, "A NEW CLASS OF BERNOULLI POLYNOMIALS ATTACHED TO POLYEXPONENTIAL FUNCTIONS AND RELATED IDENTITIES", Advanced Studies in Contemporary Mathematics, 31(2), pp.195~204 (2021), 장전수학회
  2. Broder, A. Z., "The r-Stirling numbers", Discrete Math, 49(3), pp.241~259 (1984)
  3. Carlitz, L., "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
  4. Comtet, L., "Advanced combinatorics. The art of finite and infinite expansions" (1974), D. Reidel Publishing Co.
  5. 김대산, "TWO VARIABLE HIGHER-ORDER DEGENERATE FUBINI POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 21(1), pp.5~22 (2018), 장전수학회[DOI]
  6. Kim, D. S., "A note on a new type of degenerate Bernoulli numbers", Russ. J. Math. Phys, 27(2), pp.227~235 (2020)
  7. Kim, T, "Some identities on truncated polynomials associated with degenerate Bell polynomials", Russ. J. Math. Phys, 28(3), pp.342~355 (2021)
  8. Kim, T., "On some degenerate differential and degenerate difference operator", Russ. J. Math. Phys, 29(1), pp.37~47 (2022)
  9. Kim, T., "Some formulas for fully degenerate Bernoulli numbers and polynomials", arxiv, ~ (2022)
  10. Kim, T, "A note on degenerate r-Stirling numbers", J. Inequal. Appl, pp.225~236 (2020)[DOI]
  11. Kim, T., "Degenerate r-Stirling numbers and r-Bell polynomials", Russ. J. Math. Phys, 25(1), pp.44~58 (2018)
  12. 1984, , 111~
  13. Yilmaz Simsek, "IDENTITIES AND RELATIONS RELATED TO COMBINATORIAL NUMBERS AND POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(1), pp.127~135 (2017), 장전수학회[DOI]

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