Detail publikace
Kummer test and regular variation
ŘEHÁK, P.
Anglický název
Kummer test and regular variation
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
en
Originální abstrakt
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.
Anglický abstrakt
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.
Klíčová slova anglicky
Kummer test; Regularly varying sequence; Karamata theorem; Time scale
Vydáno
28.02.2020
Nakladatel
SPRINGER WIEN
Místo
WIEN
ISSN
0026-9255
Ročník
192
Číslo
2
Strany od–do
419–426
Počet stran
8
BIBTEX
@article{BUT162150,
author="Pavel {Řehák},
title="Kummer test and regular variation",
year="2020",
volume="192",
number="2",
month="February",
pages="419--426",
publisher="SPRINGER WIEN",
address="WIEN",
issn="0026-9255"
}