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Lah-Bell numbers and polynomials

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In this paper, we introduce the Lah-Bell numbers and their natural extensions, namely the Lah-Bell polynomials, and derive some basic properties of such numbers and polynomials by using elementary methods. In addition, we consider the degenerate Lah-Bell numbers and polynomials as degenerate versions of the Lah-Bell numbers and polynomials.

Abstract

In this paper, we introduce the Lah-Bell numbers and their natural extensions, namely the Lah-Bell polynomials, and derive some basic properties of such numbers and polynomials by using elementary methods. In addition, we consider the degenerate Lah-Bell numbers and polynomials as degenerate versions of the Lah-Bell numbers and polynomials.

참고문헌 (15)

  1. Carlitz, "L. Some remarks on the Bell numbers", Fibonacci Quart, 18(1), pp.66~73 (1980)
  2. Carlitz, "L. Weighted Stirling numbers of the first and second kind II", Fibonacci Quart, 18(3), pp.242~257 (1980)
  3. Comtet, "Revised and enlarged edition" (1974), D. Reidel Publishing Co
  4. Kim, "T. Some identities of Bell polynomials", Sci. China Math, 58(10), pp.2095~2104 (2015)
  5. Kim, "T. A note on polyexponential and unipoly functions", Russ. J. Math. Phys, 26(1), pp.40~49 (2019)
  6. 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]
  7. Kim, T, "Degenerate polyexponential functions and degenerate Bell polynomials", J. Math. Anal. Appl, 487(2), pp.15~ (2020)
  8. 김택연, "Extended stirling polynomials of the second kind and extended Bell polynomials", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(3), pp.365~376 (2017), 장전수학회[DOI]
  9. Kim, T, "A note on some identities of new type degenerate Bell polynomials", Mathematics (2019)
  10. Liu, C, "Wuyungaowa Application of probabilistic method on Daehee sequences", Eur. J. Pure Appl. Math, 11(1), pp.69~78 (2018)
  11. Luo, Y.-N, "Wuyungaowa. Some combinatorial identities about Daehee sequences", J. Combin. Math. Combin. Comput, 108, pp.75~87 (2019)
  12. Roman, S, "The umbral calculus. Pure and Applied Mathematics 111" (1984), Academic Press, Inc
  13. YILMAZ SIMSEK, "IDENTITIES ON THE CHANGHEE NUMBERS AND APOSTOL-TYPE DAEHEE POLYNOMIALS", Advanced Studies in Contemporary Mathematics, 27(2), pp.199~212 (2017), 장전수학회[DOI]
  14. Tauber, S, "Lah numbers for Fibonacci and Lucas polynomials", Fibonacci Quart, 6(5), pp.93~99 (1968)
  15. Zheng, Y, "Bivariate extension of Bell polynomials", J. Integer Seq, 22(8), pp.8~ (2019)

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