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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
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- 장전수학회 Proceedings of the Jangjeon Mathematical Society Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) 제24권 제1호
- 발행연도
- 2021.1
- 수록면
- 33 - 45 (13page)
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Many mathematicians have been studying various degenerate versions of special poly- nomials and numbers not only in some arithmetic and combinatorial aspects but also in applications to differential equations, identities of symmetry and probability theory. Moreover, umbral calculus is one of the important methods for obtaining the symmetric identities for the degenerate version of special numbers and polynomials. Recently, Kim-Kim (J. Math. Anal. Appl.(2020) 23, 124521) introduced the l -Sheffer sequence and the degenerate Sheffer sequence by replacing the l - linear functional and l - differential operator, respectively, instead of the linear functionalal and the differential operator used by Rota. This paper is divided in two parts. In the first part, we introduce a new type of degenerate poly-Frobenius-Euler polynomials and numbers, and derive several combinatorial identities related to those polynomials and numbers without by using degenerate Sheffer sequences. In the second part, we also derive various combinatorial identities related to a new type of degenerate poly-Frobenius-Euler polynomials by using degenerate Sheffer sequences. Some of them include the degenerate and other special polynomials and numbers such as the degenerate falling factorials, the degenerate Bell polynomials, the degenerate Bernoulli polynomials, the degenerate Euler polynomials, the degenerate Daehee polynomials, the Stirling number of the first and second kind, etc.
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참고문헌 (30)
참고문헌 신청
S. Araci / 2012 / A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials / Advanced Studies in Contemporary Mathematics 22(3):399~406
Carlitz, L. / 1979 / Degenerate Stirling, Bernoulli and Eulerian numbers / Utilitas Math 15:51~88
Carlitz, L. / 1980 / Weighted Stirling numbers of the first and second kind / Fibonacci Quart 18:147~162
Comtet, L. / 1974 / Advanced combinatorics. The art of finite and infinite expansions / D. Reidel Publishing Co. :xi+343
R. Dere / 2012 / Applications of umbral algebra to some special polynomials / Advanced Studies in Contemporary Mathematics 22(3):433~438
Carlitz, L. / 1979 / Degenerate Stirling, Bernoulli and Eulerian numbers / Utilitas Math 15:51~88
Carlitz, L. / 1980 / Weighted Stirling numbers of the first and second kind / Fibonacci Quart 18:147~162
Comtet, L. / 1974 / Advanced combinatorics. The art of finite and infinite expansions / D. Reidel Publishing Co. :xi+343
R. Dere / 2012 / Applications of umbral algebra to some special polynomials / Advanced Studies in Contemporary Mathematics 22(3):433~438
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