Kummer test and regular variation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F20%3APU135416" target="_blank" >RIV/00216305:26210/20:PU135416 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s00605-019-01361-y" target="_blank" >https://link.springer.com/article/10.1007/s00605-019-01361-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00605-019-01361-y" target="_blank" >10.1007/s00605-019-01361-y</a>
Alternative languages
Result language
angličtina
Original language name
Kummer test and regular variation
Original language description
We establish relations among the Kummer test, certain generalization of discrete regular variation, and regular variation on time scales. More precisely, we give a new interpretation (including new proof) of the Kummer test which detects convergence of series. We show that the limit relation from the Kummer test can be rewritten in terms of recently introduced concept of refined regularly varying sequences with respect to an auxiliary sequence tau. The theory of such sequences can be developed by transforming them into the new time scale T = tau(N), which then enables us to utilize the existing results for regularly varying functions on time scales. Replace this sentence by "In particular, the Karamata type theorem and the representation for refined regularly varying sequences yield not only the Kummer test, but provide also asymptotic formulae for the partial sums of series and the representation for the sequences satisfying the Kummer test.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA20-11846S" target="_blank" >GA20-11846S: Differential and difference equations of real orders: Qualitative analysis and its applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Monatshefte fuer Mathematik
ISSN
0026-9255
e-ISSN
1436-5081
Volume of the periodical
192
Issue of the periodical within the volume
2
Country of publishing house
AT - AUSTRIA
Number of pages
8
Pages from-to
419-426
UT code for WoS article
000505429900001
EID of the result in the Scopus database
2-s2.0-85077559820