2009/01/12 by Roland Bacher, Bacher, Roland, Philippe Flajolet +1
Mathematics · #05A15 #33E05 #41A21 #42C05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #math.CA #math.CO #math.NT #msc:05A15 #msc:33E05 #msc:41A21 #msc:42C05
paper · pdf · doi:10.48550/arxiv.0901.1379
24 pages; with correction of typos and minor revision. To appear in The Ramanujan Journal
openalex publication_date 2009/01/12 · arxiv created 2009/05/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This study presents miscellaneous properties of pseudo-factorials, which are numbers whose recurrence relation is a twisted form of that of usual factorials. These numbers are associated with special elliptic functions, most notably, a Dixonian and a Weierstrass function, which parametrize the Fermat cubic curve and are relative to a hexagonal lattice. A continued fraction expansion of the ordinary generating function of pseudo-factorials, first discovered empirically, is established here. This article also provides a characterization of the associated orthogonal polynomials, which appear to form a new family of "elliptic polynomials", as well as various other properties of pseudo-factorials, including a hexagonal lattice sum expression and elementary congruences.