2024/06/17 by Taekyun Kim, Kim, Taekyun, Dae San Kim +1
Engineering · Mathematics · Physics and Astronomy · #11B68 #11B73 #11B83 #Advanced Mathematical Identities #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Number Theory (math.NT) #Tribology and Lubrication Engineering
paper · pdf · doi:10.48550/arxiv.2407.00061
openalex publication_date 2024/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Assume that the moment generating function of the random vari able Y exists in a neighborhood of the origin. We introduce the probabilistic multi-Stirling numbers of the second kind associated with Y and the proba bilistic multi-Lah numbers associated with Y, both of indices (k1,k2,...,kr), by means of the multiple logarithm. Those numbers are respectively probabilistic extensions of the multi-Stirling numbers of the second kind and the multi-Lah numbers which, for (k1,k2,...,kr) = (1,1,...,1), boil down respectively to the Stirling numbers of the second and the unsigned Lah numbers. The aim of this paper is to study some properties, related identities, recurrence relations and explicit expressions of those probabilistic extension numbers in connection with several other special numbers