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Show that the convergence by rows of a double series does not imply convergence by columns, but if the sum by rows, columns and reciangles all exist, then all three must be equal. Show also that the result may not be true if the convergence by rectangles is not assumed.

Show that the convergence by rows of a double series does not imply convergence by columns, but if the sum by rows, columns and reciangles all exist, then all three must be equal. Show also that the result may not be true if the convergence by rectangles is not assumed.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show that the convergence by rows of a double series does not imply convergence by columns, but if the sum by rows, columns and reciangles all exist, then all three must be equal. Show also that the result may not be true if the convergence by rectangles is not assumed.
Transcribed Image Text:Show that the convergence by rows of a double series does not imply convergence by columns, but if the sum by rows, columns and reciangles all exist, then all three must be equal. Show also that the result may not be true if the convergence by rectangles is not assumed.
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