NOTE ON EXTENDED LAH-BELL POLYNOMIALS AND DEGENERATE EXTENDED LAH-BELL POLYNOMIALS
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Kim-Kim(Proc. Jangjeon Math. Soc. 23(4) 2020) studied the Lah-Bell numbers and polynomials. Furthermore, many mathematicians have recently been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. From this point of view, we are interested in a new type of extended Lah-Bell polynomials and numbers, and the the degenerate extended Lah-Bell polynomials and numbers. The paper is divided in two parts. In the first part, we introduce a new type of the extended Lah-Bell polynomials and numbers, and derive several combinatorial identities related to thoese polynomials and numbers. Some of them include the degenerate and other special polynomials and numbers such as the Stirling number of the second kind, the derangement numbers, the Bell polynomials, the Changhee polynomials of order r, etc. In the second part, we also consider the degenerate extended Lah-Bell polynomials and numbers, and give some new explicit expressions and identities involving those polynomials and numbers.
Abstract
Kim-Kim(Proc. Jangjeon Math. Soc. 23(4) 2020) studied the Lah-Bell numbers and polynomials. Furthermore, many mathematicians have recently been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. From this point of view, we are interested in a new type of extended Lah-Bell polynomials and numbers, and the the degenerate extended Lah-Bell polynomials and numbers. The paper is divided in two parts. In the first part, we introduce a new type of the extended Lah-Bell polynomials and numbers, and derive several combinatorial identities related to thoese polynomials and numbers. Some of them include the degenerate and other special polynomials and numbers such as the Stirling number of the second kind, the derangement numbers, the Bell polynomials, the Changhee polynomials of order r, etc. In the second part, we also consider the degenerate extended Lah-Bell polynomials and numbers, and give some new explicit expressions and identities involving those polynomials and numbers.
참고문헌 (21)
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