Re: Re: A bug?......In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}]......Out[1]= 1/2
- To: mathgroup at smc.vnet.net
- Subject: [mg41685] Re: [mg41614] Re: [mg41594] A bug?......In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}]......Out[1]= 1/2
- From: Murray Eisenberg <murraye at attbi.com>
- Date: Fri, 30 May 2003 03:56:29 -0400 (EDT)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <200305291213.IAA03798@smc.vnet.net>
- Reply-to: murray at math.umass.edu
- Sender: owner-wri-mathgroup at wolfram.com
That this answer is obtained in the Student Version is irrelevant. (In fact, the same answer is obtained in the regular Mathematica 4.2.1.) The Student Version is the full regular version, uncrippled in any way. The only differences in the Student Version of which I am aware are: (i) the cost (!); (ii) footers or headers on printed pages identifying the Student Version; (iii) printed documentation does not include Wolfram's "The Mathematica Book" (but Help Browser does include the electronic version); and (iv) upgrade privileges. Andrzej Kozlowski wrote: > Sometimes what looks like a bug or plain nonsense turns out to be > simply a piece of more advanced mathematics than what you have been > considering. (That's of course one of the nice things about mathematics > :-) ) > The sum is indeed divergent in a conventional sense but there are > other (perfectly rigorous) senses (one due to Abel) in which it can be > summed to give precisely 1/2. > > (However, whether it is right for it to do so in a student version is > another matter.) > > Andrzej Kozlowski > Yokohama, Japan > http://www.mimuw.edu.pl/~akoz/ > http://platon.c.u-tokyo.ac.jp/andrzej/ > > > On Wednesday, May 28, 2003, at 05:57 pm, Mark wrote: > > >>I think that the sum does not converge. Does >>the following (from Mathematica for Students, >>v. 4.0.1) reveal a bug? If so, do you have >>any insight into this bug? >> >> >> In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}] >> >> Out[1]= 1/2 >> >> >> >> >> >>********** >>1366294709 >> >> >> > > > -- Reply to "REPLY TO" address and NOT to the "FROM" address!! Otherwise I will never see your reply!!!!!!!!!!!!!!!!!!!!!! Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305
- References:
- Re: A bug?......In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}]......Out[1]= 1/2
- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
- Re: A bug?......In[1]:= Sum[Cos[x], {x, 0, Infinity, Pi}]......Out[1]= 1/2