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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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