Re: NIntegrate of Oscillatory integrand
- To: mathgroup at smc.vnet.net
- Subject: [mg94358] Re: NIntegrate of Oscillatory integrand
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Thu, 11 Dec 2008 03:44:01 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <ghlml2$km8$1@smc.vnet.net> <gho300$t74$1@smc.vnet.net>
antononcube at gmail.com wrote:
> It seems it is better to do this integral symbolically:
>
> In[5]:= Integrate[(1/p)*(Cos[A - k*t] - Cos[A - f[k]*t]), {t, 0,
> Infinity}]
>
> Out[5]= ((1/k - 1/f[k])*Sin[A])/p
Just a note, but it seems that the above integral is computed
symbolically only from version 7.0.
In[1]:= $Version
Integrate[(1/p)*(Cos[A - k*t] - Cos[A - f[k]*t]), {t, 0, Infinity}]
Out[1]= "6.0 for Mac OS X x86 (64-bit) (May 21, 2008)"
During evaluation of In[1]:= Integrate::idiv: Integral of Cos[A-k \
t]/p-Cos[A-t f[k]]/p does not converge on {0,\[Infinity]}. >>
Out[2]= Integrate[(Cos[A - k*t] - Cos[A - t*f[k]])/p, {t, 0, Infinity}]
In[1]:= $Version
Out[1]= "7.0 for Microsoft Windows (32-bit) (November 10, 2008)"
In[2]:= Integrate[(1/p)*(Cos[A - k*t] - Cos[A - f[k]*t]), {t, 0,
Infinity}]
Out[2]= ((1/k - 1/f[k]) Sin[A])/p
>
> Anton Antonov
> Wolfram Research, Inc.
>
>
> On Dec 9, 7:00 am, ventut... at gmail.com wrote:
>> Do someone has an idea how can I do the numerical integral
>>
>> Int_0_to_inf (1/p)( Cos[ A - k t] - Cos[ A - k f(k) t]) where f(k) is
>> an arbitrary decreasing function (besselK0, or just a gaussian..)
>>
>> Oscillatory and DoubleExponential methods don't work...
>>
>> D.
>
>
Best regards,
-- Jean-Marc