RE: Infinite series problem
- To: mathgroup at smc.vnet.net
- Subject: [mg35957] RE: [mg35917] Infinite series problem
- From: "DrBob" <majort at cox-internet.com>
- Date: Fri, 9 Aug 2002 05:18:05 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
FoldList below gives an approximate asymptotic value, and the last
ListPlot hints at an asymptotic approximation for the terms (reciprocal
of the thing I'm multiplying by). NLimit might have worked just as
well, but I was checking to see if the limit could exist at all, before
trying that.
Timing[
v = (NIntegrate[Cos[Pi*#1*x]/((x/2)^2^(-1)*
(1 - x/2)^2^(-1)), {x, 0, 1}] & ) /@ Range[100]; ]
ListPlot[v]
v2 = 1/(2^(1/2)*(Pi*Range[100])^2*v);
FoldList[Plus, 0, v2]
ListPlot[(v2*(#1/2.1)*Log[#1]^2.2 & )[
Range[100]]]
Bobby Treat
-----Original Message-----
From: Seung Soon Jang [mailto:jsshys at wag.caltech.edu]
To: mathgroup at smc.vnet.net
Subject: [mg35957] [mg35917] Infinite series problem
Hi, Group,
I am just beginner to start using Mathematica to solve my problem.
MY goal is to get some asymptotic value of the following series. But it
doesn't give the answer and
I have no clue how to resolve the error message I met.
Please give me the idea to go through this hard thing.
Thanks,
Seung Soon
In[9]:=
Sum[1/(2^(0.5)*(Pi*k)^2*
NIntegrate[(x/2)^(-0.5)*(1-(x/2))^(-0.5)*Cos[Pi*k*x],{x,0,1}]),{k,1,
Infinity}]
NIntegrate::inum: Integrand 2.3094 Cos[1.5708 k] is not numerical at {x}
= \
{0.5}.
NIntegrate::inum: Integrand 2.3094 Cos[1.5708 k] is not numerical at {x}
= \
{0.5}.
NIntegrate::inum: Integrand 2.3094 Cos[1.5708 k] is not numerical at {x}
= \
{0.5}.
General::stop: Further output of NIntegrate::inum will be suppressed
during \
this calculation.
--
----------------------------------------------------------
Seung Soon Jang, Ph.D.
California Institute of Technology
Chemistry 139-74
Pasadena, CA 91125
TEL) 1-626-395-8147
FAX) 1-626-585-0917
e-mail) jsshys at wag.caltech.edu
home page) http://www.wag.caltech.edu/home/jsshys
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