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Some new identities and formulas for higher-order combinatorial-type numbers and polynomials

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The main purpose of this paper is to provide various identities and formulas for higherorder combinatorial-type numbers and polynomials with the help of generating functions and their both functional equations… Click to show full abstract

The main purpose of this paper is to provide various identities and formulas for higherorder combinatorial-type numbers and polynomials with the help of generating functions and their both functional equations and derivative formulas. The results of this paper comprise some special numbers and polynomials such as the Stirling numbers of the first kind, the Cauchy numbers, the Changhee numbers, the Simsek numbers, the Peters poynomials, the Boole polynomials, the Simsek polynomials. Finally, remarks and observations on our results are given.

Keywords: numbers polynomials; combinatorial type; type numbers; identities formulas; new identities

Journal Title: Filomat
Year Published: 2020

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