Re: Is there anything wrong?
- To: mathgroup at smc.vnet.net
- Subject: [mg78853] Re: Is there anything wrong?
- From: dimitris <dimmechan at yahoo.com>
- Date: Wed, 11 Jul 2007 06:10:52 -0400 (EDT)
- References: <f6qdq3$9ll$1@smc.vnet.net>
In fact we have just met a whole family of bugs!
In[125]:=
(Integrate[x^#1*Log[1 + Exp[-x]/Sqrt[x]], {x, 0, Infinity}] & ) /@
Range[0, 5] (*and so on!*)
Out[125]=
{Pi^2/6, 3*Zeta[3], (7*Pi^4)/45, 90*Zeta[5], (248*Pi^6)/315,
7560*Zeta[7]}
In[126]:=
N[%]
Out[126]=
{1.6449340668482262, 3.606170709478783, 15.152525271955932,
93.32349796290328, 756.90323811643, 7623.120537007336}
In[127]:=
(NIntegrate[x^#1*Log[1 + Exp[-x]/Sqrt[x]], {x, 0, Infinity}] & ) /@
Range[0, 5]
Out[127]=
{1.0179913870581465, 0.7444352948689439, 1.2362578807743858,
3.218067057690444, 11.46274144712573, 51.99108002709199}
(at least at version 5.2; but since Pi^2/6 is also returned in version
6, I am quite
sure that the results will exist in version 6 also...)
Dimitris
Budaoy :
> I have a problem in calculating this integral shown below(I've posted
> this question before, but I typed Exp[-x] as Exp[x] incorrectly so you
> have figured out both of them were not converge):
>
> Integrate[Log[1+Exp[-x]/Sqrt[x]],{x,0,Infinity}]
> Pi^2/6
>
> N[%]
> 1.64493
>
> NIntegrate[Log[1+Exp[-x]/Sqrt[x]],{x,0,Infinity}]
> 1.01799
>
> Where does this difference come from and which one is correct?