Degenerate ordered Bell numbers and polynomials associated with umbral calculus

Volume 10, Issue 10, pp 5142--5155

Publication Date: 2017-10-12

http://dx.doi.org/10.22436/jnsa.010.10.02

Authors

Taekyun Kim - Department of Mathematics, College of Science Tianjin Polytechnic University, Tianjin 300160, China
Dae San Kim - Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
Gwan-Woo Jang - Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
Lee-Chae Jang - Graduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea

Abstract

In this paper, we study degenerate ordered Bell polynomials with the viewpoint of Carlitz's degenerate Bernoulli and Euler polynomials and derive by using umbral calculus some properties and new identities for the degenerate ordered Bell polynomials associated with special polynomials.

Keywords

Degenerate ordered Bell polynomial, umbral calculus, Euler polynomials

References

[1] E. T. Bell, Postulational bases for the umbral calculus, Amer. J. Math., 62 (1940), 717–724.
[2] L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math., 15 (1979), 51–88.
[3] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, D. Reidel Publishing, Holland, (1974).
[4] R. Dere, Y. Simsek, Applications of umbral algebra to some special polynomials, Adv. Stud. Contemp. Math., 22 (2012), 433–438.
[5] A. Di Crescenzo, G.-C. Rota, On umbral calculus, Ricerche Mat., 43 (1994), 129–162.
[6] D. V. Dolgiń≠, D. S. Kim, T. Kim, Korobov polynomials of the first kind, Sb. Math., 208 (2017), 60–74.
[7] T. Kim, Identities involving Laguerre polynomials derived from umbral calculus, Russ. J. Math. Phys., 21 (2014), 36–45.
[8] D. S. Kim, T. Kim, J. J. Seo, Higher-order Daehee polynomials of the first kind with umbral calculus, Adv. Stud. Contemp. Math., 24 (2014), 5–18.
[9] S. Roman, The theory of the umbral calculus, J. Math. Anal. Appl., 95 (1983), 528–563.
[10] S. Roman, The umbral calculus, Academic Press, New York, (1984).
[11] G. C. Rota, B. D. Taylor, An introduction to the umbral calculus, Analysis, geometry and groups: a Riemann legacy volume, Hadronic Press, Palm Harbor, (1993).
[12] G. C. Rota, B. D. Taylor, The classical umbral calculus, SIAM J. Math. Anal., 25 (1994), 694–711.

Downloads

XML export