<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

Double Series and Sums

Gifu National College of Technology Gifu, Japan

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

{"article-title":"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...

Double Series and Sums

Published Online: Mar 30, 2014

Page range: 57 - 68

DOI: https://doi.org/10.2478/forma-2014-0006

Keywords
double series

© by Noboru Endou

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Double Series and Sums

Published Online: Mar 30, 2014

Page range: 57 - 68

DOI: https://doi.org/10.2478/forma-2014-0006

Keywordsdouble series

© by Noboru Endou

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Keywords
double series