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. ---------------------------------------------------------------------------- ------- 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: rvarad...@jhmi.edu Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ---------------------------------------------------------------------------- -------- -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of A Achilleos Sent: Tuesday, May 05, 2009 10:18 AM To: r-help@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...@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...@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@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > ---------------------- A Achilleos ma...@bristol.ac.uk ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.