Harmonic–Multifactorial Identity via Gamma and Pochhammer Structures

Zenodo (CERN European Organization for Nuclear Research) 2026 Preprint Open access

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Authors: Florent OUEDRAOGO
DOI: 10.5281/zenodo.18381866
Cited by: 0

Abstract

We establish a closed-form identity linking ratios of multifactorials to finite weighted sums involving harmonic number differences. This identity unifies factorial and double-factorial cases under a Gamma–Pochhammer framework. The proof relies on Gamma function reductions and a finite hypergeometric summation identity, with digamma reformulations and asymptotic consequences. Keywords: Multifactorials, Gamma Function, Harmonic Numbers, Hypergeometric Series, Special Functions, Number Theory.

Fields of Study & Subjects

Advanced Mathematical Identities Analytic Number Theory Research Mathematical functions and polynomials

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
27 January 2026
Language
EN
Document type
Preprint