Productly linearly independent sequences

Jaroslav Hančl; Katarína Korčeková; Lukáš Novotný

doi:10.1556/012.2015.52.3.1315

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 52: Issue 3

Productly linearly independent sequences

Authors:

Jaroslav Hančl

Jaroslav Hančl Department of Mathematics and Centre of Excellence IT4Innovation, division of UO, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1,, Czech Republic

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hancl@osu.cz

Katarína Korčeková

Katarína Korčeková Department of Mathematics and Centre of Excellence IT4Innovation, division of UO, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1,, Czech Republic

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katarina.korcekova@osu.cz

, and

Lukáš Novotný

Lukáš Novotný Department of Mathematics and Centre of Excellence IT4Innovation, division of UO, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1,, Czech Republic

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lukas.novotny@osu.cz

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Pages:: 350–370

Online Publication Date:: Sep 2015

Publication Date:: 01 Sep 2015

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/012.2015.52.3.1315

Keywords:: Primary 11J72; Linear independence; infinite product

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We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

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Studia Scientiarum Mathematicarum Hungarica
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