Christiano, John G.
M.S. (Master of Science)
Department of Mathematics
Problem: The problem was to take some of the more important results concerning single infinite series and try to extend them to the double infinite series. Procedure: The procedure involved was limited entirely to reading the various sources on this topic and summarizing them in this paper. Findings and Conclusions: In many cases the properties of single series have corresponding results for double series. The n-th term of the series in term by term less than another convergent series, it is convergent; if a series is absolutely convergent, it is convergent; if a series is absolutely convergent, any rearrangement of the terms of the series is convergent; if a series of functions is term by term less than a convergent series of constraints, then the series of functions is absolutely and uniformly convergent. The greatest difference between the two types of series is that the double series can be put in a row and column array so that we can discuss a double series as being convergent by rows, columns or both. In some cases a series can be convergent by rows and divergent by columns and vise versa, we also find that the order of sensation can be reversed only if the series contains non-negative tense or if it is absolutely convergent.
Krase, Russell F., "Double infinite series" (1967). Graduate Research Theses & Dissertations. 2660.
v, 36 pages
Northern Illinois University
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