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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


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