2022/06/07 by Tatiana I. Fedoryaeva, Fedoryaeva, Tatiana I.
Mathematics · #05A10 #11B65 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2206.03007
openalex publication_date 2022/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As is well-known, a generalization of the classical concept of the factorial n! for a real number x∈ \mathbb R is the value of Euler's gamma function Γ(1+x). In this connection, the notion of a binomial coefficient naturally arose for admissible values of the real arguments. By elementary means, it is proved a number of properties of binomial coefficients \binomrα of real arguments r, α∈ \mathbb R such as analogs of unimodality, symmetry, Pascal's triangle, etc. for classical binomial coefficients. The asymptotic behavior of such generalized binomial coefficients of a special form is established.