2018/03/15 by Claudio Pita-Ruiz, Pita-Ruiz, Claudio
Chemistry · Mathematics · #11B73 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1803.05953
openalex publication_date 2018/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider generalized Stirling numbers of the second kind % Sa,b,r^αs,βs,rs,ps( p,k) , % k=0,1,… .rp+∑s=2Lrsps, where a,b,αs,βs are complex numbers, and r,p,rs,ps are non-negative integers given, s=2,… ,L. (The case a=1,b=0,r=1,rsps=0, corresponds to the standard Stirling numbers S( p,k) .) The numbers % Sa,b,r^αs,βs,rs,ps( p,k) are connected with a generalization of Eulerian numbers and polynomials we studied in previous works. This link allows us to propose (first, and then to prove, specially in the case r=rs=1) several results involving our generalized Stirling numbers, including several families of new recurrences for Stirling numbers of the second kind. In a future work we consider the recurrence and the differential operator associated to the numbers % Sa,b,r^αs,βs,rs,ps( p,k) .