Zeta function and some of its properties
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 integratio...
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University of Defence in Belgrade
2020-10-01
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| Series: | Vojnotehnički Glasnik |
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| Online Access: | https://scindeks-clanci.ceon.rs/data/pdf/0042-8469/2020/0042-84692004895F.pdf |
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doaj-6f80fc485b5040c5b071c4757cd4d88d2020-11-25T01:43:11ZengUniversity of Defence in BelgradeVojnotehnički Glasnik0042-84692217-47532020-10-0168489590610.5937/vojtehg68-28535Zeta function and some of its propertiesNicola Fabiano0https://orcid.org/0000-0003-1645-2071Independent researcher, Rome, ItalyIntroduction/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 ζ(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.https://scindeks-clanci.ceon.rs/data/pdf/0042-8469/2020/0042-84692004895F.pdfzeta functionanalytic continuationcomplex plane integration |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nicola Fabiano |
| spellingShingle |
Nicola Fabiano Zeta function and some of its properties Vojnotehnički Glasnik zeta function analytic continuation complex plane integration |
| author_facet |
Nicola Fabiano |
| author_sort |
Nicola Fabiano |
| title |
Zeta function and some of its properties |
| title_short |
Zeta function and some of its properties |
| title_full |
Zeta function and some of its properties |
| title_fullStr |
Zeta function and some of its properties |
| title_full_unstemmed |
Zeta function and some of its properties |
| title_sort |
zeta function and some of its properties |
| publisher |
University of Defence in Belgrade |
| series |
Vojnotehnički Glasnik |
| issn |
0042-8469 2217-4753 |
| publishDate |
2020-10-01 |
| description |
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 ζ(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. |
| topic |
zeta function analytic continuation complex plane integration |
| url |
https://scindeks-clanci.ceon.rs/data/pdf/0042-8469/2020/0042-84692004895F.pdf |
| work_keys_str_mv |
AT nicolafabiano zetafunctionandsomeofitsproperties |
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1715684244028653568 |