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Do you know some dedicated books for the double series manipulations and examples with them? I need some recommendation on the subject. I noticed that the manipulations with double series are very powerful when dealing with some limits, and want to use them more. Thanks.

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Not "dedicated" - but the old book by Knopp (books.google.co.uk/books/about/… - Theory and Application of Infinite Series - should have what you need. –  Old John Jul 2 '12 at 11:17
    
@Old John: hehe. That's nice! Thanks! :-) –  Chris's sis Jul 2 '12 at 11:20
    
@Old John: unfortunately, in the high school books i have there is no such example. I looked for such a book at the library, but there is nothing on this subject. I mean tackling ways for solving limits by using double series. –  Chris's sis Jul 2 '12 at 11:31
    
The only other reference that immediately comes to mind is the (very old) Whittaker and Watson. It probably has some examples and exercises. –  Old John Jul 2 '12 at 11:39
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