2015/05/18 by M. L. Glasser, Michael Milgram
Mathematics · #Advanced Mathematical Identities #Analytic function #Fractional Differential Equations Solutions #Function (biology) #Functional equation #Mathematical functions and polynomials #Range (aeronautics) #Riemann zeta function #Simple (philosophy) #Zeta function regularization #math.CA #math.CV #msc:11M26 #msc:26A09 #msc:30B40 #msc:30C15 #msc:30E20 #msc:33B99 #msc:33C47 #msc:33F99
paper · pdf · doi:10.7153/jca-2018-12-04
published as Journal Of Classical Analysis, Volume 12, Number 1, 2018,27 · 22 pages, 2 figures
arxiv created 2015/05/18 · openalex created_date 2016/06/24 · openalex publication_date 2018/01/01 · arxiv updated 2018/10/23 · openalex updated_date 2026/08/05
A Master equation has been previously obtained which allows the analytic integration of a fairly large family of functions provided that they possess simple properties. Here, the properties of this Master equation are explored, by extending its applicability to a general range of an independent parameter. Examples are given for various values of the parameter using Riemann's Zeta function as a template to demonstrate the utility of the equation. The template is then extended to the derivation of various sum rules among the zeros of the Zeta function as an example of how similar rules can be obtained for other functions.