2009/01/17 by Milan Janjić, Janjic, Milan
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications
paper · pdf · doi:10.48550/arxiv.0901.2655
openalex publication_date 2009/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown in this note that non-central Stirling numbers s(n,k,a) of the first kind naturally appear in the expansion of derivatives of the product of a power function and a logarithn function. We first obtain a recurrence relation for these numbers, and then, using Leibnitz rule we obtain an explicit formula for these numbers. We also obtain an explicit formula for s(n,1,a), and then derive several combinatorial identities related to these numbers.