A harmonic M-factorial function and applications
type: CreativeWork
description: "We offer analogs to the falling factorial and rising factorial functions for the set of harmonic numbers, as well as a mixed factorial function called the M-factorial. From these concepts, we develop a harmonic analog of the binomial coefficient and an alternate expression of the harmonic exponential function and establish several identities. We generalize from the harmonic numbers to a general time scale and demonstrate how solutions to some second order eigenvalue problems and partial dynamic equations can be constructed using power series built from the M-factorial function"--Abstract, page iii.
abstract: "We offer analogs to the falling factorial and rising factorial functions for the set of harmonic numbers, as well as a mixed factorial function called the M-factorial. From these concepts, we develop a harmonic analog of the binomial coefficient and an alternate expression of the harmonic exponential function and establish several identities. We generalize from the harmonic numbers to a general time scale and demonstrate how solutions to some second order eigenvalue problems and partial dynamic equations can be constructed using power series built from the M-factorial function"--Abstract, page iii.
author: Brigham, Reginald Alfred, II
keywords: Binomial Coefficient, Eigenvalue, Factorial, Harmonic Numbers, Time Scales, Mathematics
date modified: 2026-07-24T03:18:26Z
provider: Missouri University of Science and Technology
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Missouri University of Science and Technology