SOME IDENTITIES OF DEGENERATE r-DOWLING POLYNOMIALS OF THE SECOND KIND ARISING FROM UMBRAL CALCULUS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Recently, the author Kim and Lee [16] introduced interest- ing properties and identities for the degenerate r-Dowling polynomials and numbers associated with the degenerate r-Whitney numbers of the second kind. In this paper, we study methods for computing the ra- tional coefficients of a linear combination of the degenerate r-Dowling polynomials of the second kind with degree n by using umbral calculus, for algebraic applications of [16]. We derive some interesting identities for certain special polynomials from these coefficients. Furthermore, we explore various identities of the degenerate r-Dowling polynomials aris- ing from the falling factorials bases, the Euler polynomials bases, the Daehee polynomials bases, the degenerate r-Bell polynomials bases, the Bell polynomials bases by using umbral calculus, respectively.
Abstract
Recently, the author Kim and Lee [16] introduced interest- ing properties and identities for the degenerate r-Dowling polynomials and numbers associated with the degenerate r-Whitney numbers of the second kind. In this paper, we study methods for computing the ra- tional coefficients of a linear combination of the degenerate r-Dowling polynomials of the second kind with degree n by using umbral calculus, for algebraic applications of [16]. We derive some interesting identities for certain special polynomials from these coefficients. Furthermore, we explore various identities of the degenerate r-Dowling polynomials aris- ing from the falling factorials bases, the Euler polynomials bases, the Daehee polynomials bases, the degenerate r-Bell polynomials bases, the Bell polynomials bases by using umbral calculus, respectively.
참고문헌 (28)
- M. Benoumhani, "On Whitney numbers of Dowling lattices", Discrete Math, 159, pp.13~33 (1996)
- M. Benoumhani, "On some numbers related to Whitney numbers of Dowling lattices", Adv. Appl. Math, 19, pp.106~116 (1997)
- A.Z. Broder, "The r-Stirling numbers", Discrete Math, 49, pp.241~259 (1984)
- N.P. Cakic, "On generalized Stirling numbers and polynomials", Math. Balk, 18, pp.241~248 (2004)
- L. Carlitz, "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
- Joy Antonette D. Cillar, "A $q$-analogue of Qi formula for $r$-Dowling numbers", 대한수학회논문집, 35(1), pp.21~41 (2020), 대한수학회[DOI]
- Gi-Sang Cheon, "r-Whitney numbers of Dowling lattices", Discrete Mathematics, 312(15), pp.2337~2348 (2012), Elsevier BV[DOI]
- L. Comtet, "Advanced Combinatorics: The art of finite and infinite expansions" (1974), Reidel
- G. V. Dunne, "Bernoulli number identities from quantum field theory and topological string theory", Commun. Number Theory Phys, 7(2), pp.225~249 (2013)
- T.A. Dowling, "A class of gemometric lattices bases on finite groups", J. Combin. Theory Ser. B, 14, pp.61~86 (1973)
- I. M. Gessel, "On Mikis identities for Bernoulli numbers", J. Number Theory, 110(1), pp.75~82 (2005)
- Eszter Gyimesi, "A comprehensive study of $${\varvec{r}}$$ r -Dowling polynomials", Aequationes mathematicae, 92(3), pp.515~527 (2018), Springer Science and Business Media LLC[DOI]
- Eszter Gyimesi, "New combinatorial interpretations of r-Whitney and r-Whitney-Lah numbers", Discrete Applied Mathematics, 255, pp.222~233 (2019), Elsevier BV[DOI]
- D.S. Kim, "A note on a new type of degenerate Bernoulli numbers", Russ. J. Math. Phys, 27(2), pp.227~235 (2020)
- Dae San Kim, "Daehee numbers and polynomials", Applied Mathematical Sciences, 7, pp.5969~5976 (2013), Hikari, Ltd.[DOI]
- Hye Kyung Kim, "Some Properties of Degenerate r-Dowling Polynomials and Numbers of the Second Kind", Computer Modeling in Engineering & Sciences, 133(3), pp.825~842 (2022), Computers, Materials and Continua (Tech Science Press)[DOI]
- 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]
- T. Kim, "Degenerate Whitney numbers of the first and second kinds of Dowling lattics", Russ. J. Math. Phys., 29(3) (2022)
- T. Kim, "Some identities on the Euler numbers arising from Euler basis polynomials", Ars. Combin, 109, pp.433~446 (2013)
- 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]
- Taekyun Kim, "Degenerate r-Whitney numbers and degenerate r-Dowling polynomials via boson operators", Advances in Applied Mathematics, 140, pp.102394~ (2022), Elsevier BV[DOI]
- I. Mezo, "A new formula for the Bernoulli polynomials", Results Math., 58, pp.329~335 (2010)
- H. Miki, "A relation between Bernoulli numbers", J. Number Theory, 10(3), pp.297~302 (1978)
- S. Roman, "The umbral calculus, Pure and Applied Mathematics" (1984)
- G. -C.Rota, "On the foundations of combinatorial theory I, theory of Mobius functions", Z. Wahrscheinlichkeitstheorie, 2, pp.340~368 (1964)
- M. Shattuck, "Some combinatorial identities for the r-Dowling polynomials", Notes on Number Theory and Discrete Math, 25(2), pp.145~154 (2019)[DOI]
- K. Shiratani, "Anapplicationofp-adicconvolutions", Mem. Fac. Sci. KyushuUniv. Ser. A, 36(1), pp.73~83 (1982)
- Y. Simsek, "Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications", Fixed Point Theory and Applications, 2013, pp.87~ (2013)