SOME IDENTITIES OF DEGENERATE r-EXTENDED LAH-BELL POLYNOMIALS
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초록
In recent years, many mathematicians have studied special numbers and polynomials in a variety of ways, using several means, including generating functions, combinatorial methods, umbral calculus, p-adic analysis, differential equations, and probabilities and so on. Umbral calculus was based on modern concepts such as linear functionals, linear operators, adjoints, and so on. Recently, Kim-Kim (J. Math. Anal. Appl. (2020), 23, 124521) introduced the degenerate Sheffer sequence and the l -Sheffer sequence. In addition, many mathematicians have studied special poly- nomials and various degenerate versions of numbers in some arithmetic and combinatorial aspects, as well as applications to differential equations, identity of symmetry, and probability theory. For these point of view, this paper is divided in two parts. In the first part, we introduce the degenerate r-extended Lah-Bell polynomials and and derive several combinatorial identities related to those polynomials and numbers without using degenerate Sheffer sequences. In the second part, we also derive several combinatorial identities related to the degenerate r-extended Lah-Bell polynomials by using degenerate Sheffer sequences. Some of them include other special polynomials and numbers such as Lah numbers, r-extended Lah numbers, the degenerate Lah-Bell polynomials, the degenerate Bernoulli polynomials and numbers, the degenerate Euler polynomials and numbers, the degenerate Daehee polynomials and numbers, the degenerate Bell polynomials, the degenerate Stirling numbers of the first and second kind, and etc.
Abstract
In recent years, many mathematicians have studied special numbers and polynomials in a variety of ways, using several means, including generating functions, combinatorial methods, umbral calculus, p-adic analysis, differential equations, and probabilities and so on. Umbral calculus was based on modern concepts such as linear functionals, linear operators, adjoints, and so on. Recently, Kim-Kim (J. Math. Anal. Appl. (2020), 23, 124521) introduced the degenerate Sheffer sequence and the l -Sheffer sequence. In addition, many mathematicians have studied special poly- nomials and various degenerate versions of numbers in some arithmetic and combinatorial aspects, as well as applications to differential equations, identity of symmetry, and probability theory. For these point of view, this paper is divided in two parts. In the first part, we introduce the degenerate r-extended Lah-Bell polynomials and and derive several combinatorial identities related to those polynomials and numbers without using degenerate Sheffer sequences. In the second part, we also derive several combinatorial identities related to the degenerate r-extended Lah-Bell polynomials by using degenerate Sheffer sequences. Some of them include other special polynomials and numbers such as Lah numbers, r-extended Lah numbers, the degenerate Lah-Bell polynomials, the degenerate Bernoulli polynomials and numbers, the degenerate Euler polynomials and numbers, the degenerate Daehee polynomials and numbers, the degenerate Bell polynomials, the degenerate Stirling numbers of the first and second kind, and etc.
참고문헌 (29)
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