Double Series and Sums
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 Pr...
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| Format: | Article |
| Language: | English |
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Sciendo
2014-03-01
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| Series: | Formalized Mathematics |
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| Online Access: | https://doi.org/10.2478/forma-2014-0006 |
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doaj-d9e70f8b4fb64b179f17246bedfc2f9f2021-09-05T21:01:03ZengSciendoFormalized Mathematics1898-99342014-03-01221576810.2478/forma-2014-0006Double Series and SumsEndou Noboru0Gifu National College of Technology Gifu, JapanIn 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.https://doi.org/10.2478/forma-2014-0006double series |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Endou Noboru |
| spellingShingle |
Endou Noboru Double Series and Sums Formalized Mathematics double series |
| author_facet |
Endou Noboru |
| author_sort |
Endou Noboru |
| title |
Double Series and Sums |
| title_short |
Double Series and Sums |
| title_full |
Double Series and Sums |
| title_fullStr |
Double Series and Sums |
| title_full_unstemmed |
Double Series and Sums |
| title_sort |
double series and sums |
| publisher |
Sciendo |
| series |
Formalized Mathematics |
| issn |
1898-9934 |
| publishDate |
2014-03-01 |
| description |
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. |
| topic |
double series |
| url |
https://doi.org/10.2478/forma-2014-0006 |
| work_keys_str_mv |
AT endounoboru doubleseriesandsums |
| _version_ |
1717781773249675264 |