Re: NDSolve::ndsz question
- To: mathgroup at smc.vnet.net
- Subject: [mg63748] Re: NDSolve::ndsz question
- From: "antononcube" <antononcube at gmail.com>
- Date: Fri, 13 Jan 2006 04:48:28 -0500 (EST)
- References: <dpnqoa$6rh$1@smc.vnet.net><dpvmjv$ltf$1@smc.vnet.net> <dq53pi$aak$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
The reason that NSum returns ComplexInfinity for f[0.25] is that the
summand doesn't pass one of the NSum convergence tests. NSum does not
think that the terms of the sequence go to 0:
In[65]:= Limit[s[k, 0.25], k -> Infinity]
Out[65]= -1.0231869534531498*^-17
For f[1/4] that convergence test is passed:
In[62]:= Limit[s[k, 1/4], k -> Infinity]
This definition might work better for the sequences based on s[k,x]:
In[83]:=
ff[(x_)?NumericQ] := NSum[s[k, x], {k, 0, Infinity}, VerifyConvergence
-> False,
Method -> Fit, WorkingPrecision -> $MachinePrecision]
In[84]:=ff[0.25]
Out[84]=0.2195242695246340035`5.6218613462276545
In[85]:= ff[1/4]
Out[85]=0.219523012888461236`6.516892681223448
Anton Antonov
Wolfram Research, Inc.