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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| Format: | Article |
| Language: | English |
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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 |
| Summary: | 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. |
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| ISSN: | 0042-8469 2217-4753 |