Zeta function and some of its properties-Reference-Cited by-同舟云学术

Zeta function and some of its properties

Published:2020 Issue:4 Volume:68 Page:895-906
ISSN:0042-8469
Container-title:Vojnotehnicki glasnik
language:en
Short-container-title:Vojnotehnički glasnik

Author:

Fabiano Nikola^ORCID

Abstract

Introduction/purpose: Some properties of the zeta function will be shown as well as its applications in calculus, in particular the "golden nugget formula" for the value of the infinite sum 1 + 2 + 3 + · · · . Some applications in physics will also be mentioned. Methods: Complex plane integrations and properties of the Gamma function will be used from the definition of the function to its analytic extension. Results: From the original definition of the z(s) function valid for s > 1 a meromorphic function is obtained on the whole complex plane with a simple pole in s = 1. Conclusion: The relevance of the zeta function cannot be overstated, ranging from the infinite series to the number theory, regularization in theoretical physics, the Casimir force, and many other fields.

Publisher

Centre for Evaluation in Education and Science (CEON/CEES)

Link

https://scindeks-clanci.ceon.rs/data/pdf/0042-8469/2020/0042-84692004895F.pdf

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