본문 바로가기
KERD
논문KCI 등재

On partially degenerate Bell numbers and polynomials

김대산|DMITRY V. DOLGY|김택연
장전수학회 (Jangjeon Mathematical Society)|2017.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제20권 제3호|pp. 337-346|DOI 10.17777/pjms.2017.20.3.003

2

조회

0

다운로드

15

인용

0

참고문헌

키워드

partially degenerate Bell numbers and polynomialsStirling num-ber of the rst kindStirling number of the second kind.
주제분류수학

초록

Recently, several authors have studied Bell numbers and poly- nomials, also called Tochard polynomials or exponential polynomials, by using and without using umbral calculus. In this paper, as a degenerate ver- sion of ordinary Bell numbers and polynomials, we introduce the partially degenerate Bell numbers and polynomials and give some new identities for those numbers and polynomials related with Stirling numbers of the rst and second kind.

Abstract

Recently, several authors have studied Bell numbers and poly- nomials, also called Tochard polynomials or exponential polynomials, by using and without using umbral calculus. In this paper, as a degenerate ver- sion of ordinary Bell numbers and polynomials, we introduce the partially degenerate Bell numbers and polynomials and give some new identities for those numbers and polynomials related with Stirling numbers of the rst and second kind.

참고문헌 (20)

  1. G. E. Andrews, "The Theory of Partitions" (1998), Cambridge University Press
  2. E. T. Bell, "Exponential polynomials", Ann. of Math., 35, pp.258~277 (1934)
  3. J. Brillhart, "Mathematical Notes: Note on the Single Variable Bell polynomials", Amer. Math. Monthly, 74(6), pp.695~696 (1967)
  4. F. Brafman, "On Touchard polynomials", Canad. J. Math., 9, pp.191~193 (1957)
  5. L. Carlitz, "Some polynomials of Touchard connected with Bernoulli numbers", Canad. J. Math., 9, pp.188~190 (1957)
  6. L. Carlitz, "Some arithmetic properties of the Bell polynomials", Bull. Amer. Math. Soc., 71, pp.143~144 (1965)
  7. L. Carlitz, "Arithmetic properties of the Bell polynomials", J. Math. Anal. Appl., 15, pp.33~52 (1966)
  8. O. Chrysaphinou, "On Touchard polynomials", Discrete Math., 54(2), pp.143~152 (1985)
  9. L. Comtet, "Advanced Combinatorics" (1974), Kluwer
  10. H. W. Gould, "Characterization of (c)-Riordan arrays, Gegenbauer-Humbert-type polynomial sequences, and (c)-Bell polynomials", J. Math. Res. Appl., 33, pp.505~527 (2013)
  11. Herscovici O, "Identities involving Touchard polynomials derived from umbral calculus", Adv Stud Comtemp. Math, 25, pp.39~46 (2015)
  12. L.-C. Jang, "Some identities of Bell polynomials", J. Comput. Anal. Appl., 20(3), pp.584~589 (2016)
  13. Dae San Kim, "On degenerate Bell numbers and polynomials", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 111(2), pp.435~446 (2017), Springer Nature[DOI]
  14. D. S. Kim, "Some identities of Bell polynomials", Sci. China Math., 58(10), pp.2905~2104 (2016)
  15. D. S. Kim, "On degenerate Bell numbers and polynomials", Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 111(2), pp.435~446 (2017)
  16. T. Kim, "On λ-Bell polynomials associated with umbral calculus", Russ. J. Math. Phys., 24(10), pp.69~78 (2017)
  17. J. Riordan, "An Introduction to Combinatorial Analysis" (1980), Princeton University Press
  18. S. Roman, "The Umbral Calculus" (1984), Academic Press
  19. M. Wyman, "On some polynomials of Touchard", Canad. J. Math., 8, pp.321~322 (1956)
  20. Z. Zhang, "Note on some identities related to the partial Bell polynomials", Tamsui Oxf. J. Inf. Math. Sci., 28, pp.39~48 (2012)

관련 논문AI추천

DEGENERATE COMPLETE BELL POLYNOMIALS AND NUMBERS김택연장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제4호ON DEGENERATE BELL POLYNOMIALS ASSOCIATED WITH SPECIAL NUMBERS AND POLYNOMIALS권종겸, 김대산, 김태균, UITAE PARK장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제3호ON THE EXTENSION OF DEGENERATE STIRLING POLYNOMIALS OF THE SECOND KIND AND DEGENERATE BELL POLYNOMIALS권혁인, 김태균, 장관우장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제2호DEGENERATE ORDERED BELL NUMBERS AND POLYNOMIALS김태균장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제2호Some identities of partially degenerate Bell polynomials arising from differential equations김태균, 장관우장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제2호SOME FORMULAS OF ORDERED BELL NUMBERS AND POLYNOMIALS ARISING FROM UMBRAL CALCULUS김대산, 김택연, 장광우장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2017 · 제20권 제4호

이 간행물의 다른 논문 (14건)

A note on degenerate stirling polynomials of the second kind김택연pp. 319-332Approximate automorphisms of solvable linear connected Lie groupsA. I. Shternpp. 333-336Complete left ideals in ternary semigroupsBINDU.P, Srinivasarao Thota, MADHUSUDHAVA RAO.D, SARALA. Ypp. 347-352Distance majorization integrity of graphsSULTAN SENAN MAHDE, Veena Mathadpp. 353-364Extended stirling polynomials of the second kind and extended Bell polynomials김대산, 장광우, 김택연pp. 365-376
원문 보기