Degenerate falling factorial polynomials
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In this paper, we will introduce degenerate falling factorial polynomials as a degenerate version of the usual falling factorial polynomials. We will use generating functions, umbral calculus and the recently introduced notion of composita in order to derive explicit expressions, some properties, recurrence relations and connections with other familiar families of polynomials. Along the way, we will introduce degenerate Stirling numbers of the first kind, some of which properties are investigated.
Abstract
In this paper, we will introduce degenerate falling factorial polynomials as a degenerate version of the usual falling factorial polynomials. We will use generating functions, umbral calculus and the recently introduced notion of composita in order to derive explicit expressions, some properties, recurrence relations and connections with other familiar families of polynomials. Along the way, we will introduce degenerate Stirling numbers of the first kind, some of which properties are investigated.
참고문헌 (13)
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