2004/05/31 by G. Della Riccia, Giacomo Della Riccia, Della Riccia, G.
Mathematics · Physics and Astronomy · #05A10 (Primary) #05A15 (Secondary) #05A19 #60E10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A10 #msc:05A15 #msc:05A19 #msc:60E10
paper · pdf · doi:10.48550/arxiv.math/0405594
11 pages
arxiv created 2004/05/31 · openalex publication_date 2004/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inversion formulas have been found, converting between Stirling, tanh and Lah numbers. Tanh and Lah polynomials, analogous to the Stirling polynomials, have been defined and their basic properties established. New identities for Stirling and tangent numbers and polynomials have been derived from the general inverse relations. In the second part of the paper, it has been shown that if shifted-gamma probability densities and negative binomial distributions are matched by equating their first three semi-invariants (cumulants), then the cumulants of the two distributions are related by a pair of reciprocal linear combinations equivalent to the inversion formulas established in the first part.