Cauchy product
in [Math]
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From: Eric on 15 Apr 2010 14:21 Find a series that does not absolutely converge but when we rewite this series by Cauchy Product then the series diverge.
From: Robert Israel on 15 Apr 2010 15:05 Eric <eric955308(a)yahoo.com.tw> writes: > Find a series that does not absolutely converge but when we rewite > this series by Cauchy Product then the series diverge. What do you mean by "rewrite this series by Cauchy Product"? Do you mean the series converges (but not absolutely) and is the Cauchy product of two series which both diverge? For example, take a_n = n'th Maclaurin series coefficient of (1+x)*ln(1+x)/(1-x) b_n = n'th Maclaurin series coefficient of (1-x)/(1+x) whose Cauchy product is c_n = n'th Maclaurin series coefficient of ln(1+x) -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada
From: Eric on 15 Apr 2010 22:52 On 4æ16æ¥, ä¸å3æ05å, Robert Israel <isr...(a)math.MyUniversitysInitials.ca> wrote: > Eric <eric955...(a)yahoo.com.tw> writes: > > Find a series that does not absolutely converge but when we rewite > > this series by Cauchy Product then the series diverge. > > What do you mean by "rewrite this series by Cauchy Product"? > Do you mean the series converges (but not absolutely) and is the > Cauchy product of two series which both diverge?  For example, take > > a_n = n'th Maclaurin series coefficient of (1+x)*ln(1+x)/(1-x) > b_n = n'th Maclaurin series coefficient of (1-x)/(1+x) > > whose Cauchy product is > > c_n = n'th Maclaurin series coefficient of ln(1+x) > -- > Robert Israel        isr...(a)math..MyUniversitysInitials.ca > Department of Mathematics     http://www.math.ubc.ca/~israel > University of British Columbia       Vancouver, BC, Canada Many thanks for your help, Eric Hsiao
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