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SOME IDENTITIES ON THE FULLY DEGENERATE BELL POLYNOMIALS OF THE SECOND KIND

임동규|마민영
장전수학회 (Jangjeon Mathematical Society)|2020.01|Advanced Studies in Contemporary Mathematics|제30권 제1호|pp. 145-154

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참고문헌

키워드

differential equationdegenerate Bell numberdegenerate Bell number of the second kind
주제분류수학

초록

Recently many interesting works are done on the degenerate Bell polynomials, which are intiated by T. Kim and D. S. Kim. And later T. Kim et al. studied on the partially degenerate Bell polynomials. Also D. V. Dolgy et al. de ned and studied fully degenerate Bell polynomials. Recently, S. Pyo and T. Kim studied some identities on the fully degenerate Belly polynomials by using di erential equations. In the paper, we consider new denenerating approach to the Bell polynomials which is called fully degenerate Bell polynomials of the second kind. We study some identities from the generating function and specially by using the di erential equations on those polynomials. We derive some identities of our fully degenerate Bell polynomials of the second kind, which related with higher order Daehee polynomials and higher order Bernoulli numbers.

Abstract

Recently many interesting works are done on the degenerate Bell polynomials, which are intiated by T. Kim and D. S. Kim. And later T. Kim et al. studied on the partially degenerate Bell polynomials. Also D. V. Dolgy et al. de ned and studied fully degenerate Bell polynomials. Recently, S. Pyo and T. Kim studied some identities on the fully degenerate Belly polynomials by using di erential equations. In the paper, we consider new denenerating approach to the Bell polynomials which is called fully degenerate Bell polynomials of the second kind. We study some identities from the generating function and specially by using the di erential equations on those polynomials. We derive some identities of our fully degenerate Bell polynomials of the second kind, which related with higher order Daehee polynomials and higher order Bernoulli numbers.

참고문헌 (17)

  1. E. T. Bell, "Exponential polynomials", Ann. of Math, 35(2), pp.285~277 (1934)
  2. J. Brillhart, "Mathematical Notes : Note on the single variable Bell polynomials", Amer. Math. Monthly, 74(6), pp.695~696 (1967)
  3. L. Carlitz, "Degenerate Stirling, Bernoulli and Eulerian numbers", Utilitas Math, 15, pp.51~88 (1979)
  4. L. Carlitz, "Some arithmetic properties of the Bell polynomials", Bull. Amer. Math. Soc, 71, pp.143~144 (1965)
  5. L. Carlitz, "Arithmetic properties of the Bell polynomials", J. Math. Anal. Appl, 15, pp.33~52 (1966)
  6. D. V. Dolgy, "On fully degenerate Bell numbers and polynomials", ~
  7. L.-C. Jang, "Some identities of Bell polynomials", J. Comput. Anal. Appl, 20(3), pp.584~589 (2016)
  8. D. S. Kim, "Some identities of Bell polynomials", Sci. China Math, 58(10), pp.2095~2104 (2015)
  9. D. S. Kim, "On degenerate Bell numbers and polynomials", RACSAM Rev. R. Acad. A., 111(2), pp.435~446 (2017)
  10. T. Kim, "Degenerate Laplace transform and degenerate gamma function", Russ. J. Math. Phys, 24(2), pp.241~248 (2017)
  11. 김택연, "On partially degenerate Bell numbers and polynomials", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(3), pp.337~346 (2017), 장전수학회[DOI]
  12. T. Kim, "Extended degenerate Stirling numbers of the second kind and extended degenerate Bell polynomials", Util. Math, 106, pp.11~21 (2018)
  13. 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]
  14. 김택연, "DEGENERATE COMPLETE BELL POLYNOMIALS AND NUMBERS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(4), pp.533~543 (2017), 장전수학회[DOI]
  15. 표성수, "Some identities of fully degenerate bell polynomials arising from differential equations", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 22(2), pp.359~365 (2019), 장전수학회
  16. 장관우, "REVISIT OF IDENTITIES FOR DAEHEE NUMBERS ARISING FROM NONLINEAR DIFFERENTIAL EQUATIONS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 20(2), pp.163~177 (2017), 장전수학회[DOI]
  17. 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]

관련 논문AI추천

Some identities of fully degenerate bell polynomials arising from differential equations김태균, 표성수장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제2호ON THE EXTENSION OF DEGENERATE STIRLING POLYNOMIALS OF THE SECOND KIND AND DEGENERATE BELL POLYNOMIALS권혁인, 김태균, 장관우장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제2호SOME IDENTITIES ON DEGENERATE BELL POLYNOMIALS AND THEIR RELATED IDENTITIES김대산, 김태균장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2022 · 제25권 제1호ON DEGENERATE BELL POLYNOMIALS ASSOCIATED WITH SPECIAL NUMBERS AND POLYNOMIALS권종겸, 김대산, 김태균, UITAE PARK장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제3호Some identities of partially degenerate Bell polynomials arising from differential equations김태균, 장관우장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제2호SOME IDENTITIES FOR DEGENERATE EULER NUMBERS AND POLYNOMIALS ARISING FROM DEGENERATE BELL POLYNOMIALS권혁인, 김태균, 서종진, Dmitry V. Dolgy장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제3호

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