Your integrand is smooth.
What are the limits of integration: 0 to 1 or 0 to infinity? Main challenge
is that it is increasingly oscillatory as x and/or t increase. You can find
the zeros of the cosine function and add up the integrals between successive
zeros. In what context does this inttegral arise? It must have been
studied well using asymptotic approximation and such.
Ravi.
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Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625
Email: rvaradhan at jhmi.edu
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of A Achilleos
Sent: Tuesday, May 05, 2009 10:18 AM
To: r-help at r-project.org
Subject: Re: [R] FOURIER INTEGRALS IN R
Ok thanks..
No, my function is not smooth.
Actually, I am dealing with an integral having the following form, for
example:
\int cos(tx) (1-t^2)^3 \exp(0.5*t^2) dt
I want to estimate this Fourier Cosine integral for a given value of x.
Thanks for the help.
AA
On Tue, May 5, 2009 2:34 am, andrew wrote:> integrate offers some one-dimensional algorithms, but you need to
> start with a smooth function to get it to converge properly. ?With a
> cosine integral, there may be certain routines that offer better value
> for money: the Clenshaw-Curtis integration, or perhaps the FFT. ?You
> would have to recast your problem by doing some sort of substitution.
>
> Perhaps post some latex code to show the exact type of integral you
> are wanting to calculate.
>
> Regards,
>
> On May 5, 6:32?am, "Achilleas Achilleos" <ma... at
bristol.ac.uk> wrote:
>> Hi,
>>
>> I am wondering whether there exist any function in R (any package)
>> that calculates Fourier Integrals.
>>
>> Particularly, I am interested for estimation of a Cosine Fourier
>> integral...
>>
>> I would be much obliged if you could help me on this..
>>
>> Thanks.
>>
>> Andreas
>>
>> --
>>
>> ______________________________________________
>> R-h... at r-project.org mailing
>> listhttps://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting
>> guidehttp://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
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>
----------------------
A Achilleos
maxaa at bristol.ac.uk
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