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http://hdl.handle.net/11320/3702
Tytuł: | Double Series and Sums |
Autorzy: | Endou, Noboru |
Słowa kluczowe: | double series |
Data wydania: | 2014 |
Data dodania: | 9-gru-2015 |
Wydawca: | De Gruyter Open |
Źródło: | Formalized Mathematics, Volume 22, Issue 1, 2014, Pages 57-68 |
Abstrakt: | In this paper the author constructs several properties for double series and its convergence. The notions of convergence of double sequence have already been introduced in our previous paper [18]. In section 1 we introduce double series and their convergence. Then we show the relationship between Pringsheim-type convergence and iterated convergence. In section 2 we study double series having non-negative terms. As a result, we have equality of three type sums of non-negative double sequence. In section 3 we show that if a non-negative sequence is summable, then the sequence of rearrangement of terms is summable and it has the same sums. In the last section two basic relations between double sequences and matrices are introduced. |
Afiliacja: | Gifu National College of Technology Gifu, Japan |
Sponsorzy: | This work was supported by JSPS KAKENHI 23500029. |
URI: | http://hdl.handle.net/11320/3702 |
DOI: | 10.2478/forma-2014-0006 |
ISSN: | 1426-2630 1898-9934 |
Typ Dokumentu: | Article |
Występuje w kolekcji(ach): | Formalized Mathematics, 2014, Volume 22, Issue 1 |
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forma-2014-0006.pdf | 266,98 kB | Adobe PDF | Otwórz |
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