Re: [R] Off topic --- help in locating a source.
Rolf, The formula can be found in section 1.44-1.45 'Trigonometric (Fourier) series' of the famous book: Gradshteyn I.S and Ryzhik I.M. "Tables of Integrals, Series, and Products". Academic Press Inc. 4th printing. London 1983. Which is a translation of the Russian book from 1963. Hope it helps, Augusto Augusto Sanabria. MSc, PhD. Mathematical Modeller Risk Research Group Geospatial & Earth Monitoring Division Geoscience Australia (www.ga.gov.au) Cnr. Jerrabomberra Av. & Hindmarsh Dr. Symonston ACT 2609 Ph. (02) 6249-9155 -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Rolf Turner Sent: Thursday, 18 May 2006 5:27 AM To: r-help@stat.math.ethz.ch Subject: [R] Off topic --- help in locating a source. Apologies for the off-topic question; as usual I'm trying to draw upon the unparalleled knowledge and sagacity of the r-help list. Please reply off-list if you can help me out. A collaborator of mine found a formula we need, on sheets which he had photocopied out of a book, some years ago. He cannot remember which book (he's getting to be as senile and forgetful as I am, poor bloke!). He thinks it was (and it appears to have been) a large encylopedic tome devoted to extensive tables of formulae, integrals and series, and stuff like that. The formula in question is oo 1 1 1 SUM --- cos(k*x) = --- ln () 0 < x < 2*pi . k=1 k 2 2*(1 - cos(x)) (I.e. the right hand side is a function whose Fourier coefficients are 1/k, k > 0). Note that ``oo'' is my attempt to render the infinity symbol in ASCII. Does anyone know of a source where this formula may found/cited? (It doesn't *have* to be the same source from which my collaborator originally copied it!) It must be well-known/in lots of books, mustn't it? Said he, hopefully. Thanks for any assistance. cheers, Rolf Turner [EMAIL PROTECTED] __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Off topic --- help in locating a source.
If a web site is suffiicent then: http://functions.wolfram.com/ElementaryFunctions/Cos/23/02/ On 5/17/06, Rolf Turner <[EMAIL PROTECTED]> wrote: > Apologies for the off-topic question; as usual I'm trying to draw > upon the unparalleled knowledge and sagacity of the r-help list. > Please reply off-list if you can help me out. > > A collaborator of mine found a formula we need, on sheets which he had > photocopied out of a book, some years ago. He cannot remember which > book (he's getting to be as senile and forgetful as I am, poor > bloke!). He thinks it was (and it appears to have been) a large > encylopedic tome devoted to extensive tables of formulae, integrals > and series, and stuff like that. > > The formula in question is > > oo 1 1 1 >SUM --- cos(k*x) = --- ln () 0 < x < 2*pi . >k=1 k 2 2*(1 - cos(x)) > > (I.e. the right hand side is a function whose Fourier coefficients > are 1/k, k > 0). > > Note that ``oo'' is my attempt to render the infinity symbol in > ASCII. > > Does anyone know of a source where this formula may found/cited? > (It doesn't *have* to be the same source from which my collaborator > originally copied it!) It must be well-known/in lots of books, > mustn't it? Said he, hopefully. > > Thanks for any assistance. > >cheers, > >Rolf Turner >[EMAIL PROTECTED] > > __ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html > __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Re: [R] Off topic --- help in locating a source.
I would check one of the following: 1. Abramowitz and Stegun's HMF 2. Jolley's "Summation of Series" 3. Knopp's book on Infinite Series. 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: [EMAIL PROTECTED] -- > -Original Message- > From: [EMAIL PROTECTED] [mailto:r-help- > [EMAIL PROTECTED] On Behalf Of Rolf Turner > Sent: Wednesday, May 17, 2006 3:27 PM > To: r-help@stat.math.ethz.ch > Subject: [R] Off topic --- help in locating a source. > > Apologies for the off-topic question; as usual I'm trying to draw > upon the unparalleled knowledge and sagacity of the r-help list. > Please reply off-list if you can help me out. > > A collaborator of mine found a formula we need, on sheets which he had > photocopied out of a book, some years ago. He cannot remember which > book (he's getting to be as senile and forgetful as I am, poor > bloke!). He thinks it was (and it appears to have been) a large > encylopedic tome devoted to extensive tables of formulae, integrals > and series, and stuff like that. > > The formula in question is > > oo 1 1 1 > SUM --- cos(k*x) = --- ln () 0 < x < 2*pi . > k=1 k 2 2*(1 - cos(x)) > > (I.e. the right hand side is a function whose Fourier coefficients > are 1/k, k > 0). > > Note that ``oo'' is my attempt to render the infinity symbol in > ASCII. > > Does anyone know of a source where this formula may found/cited? > (It doesn't *have* to be the same source from which my collaborator > originally copied it!) It must be well-known/in lots of books, > mustn't it? Said he, hopefully. > > Thanks for any assistance. > > cheers, > > Rolf Turner > [EMAIL PROTECTED] > > __ > R-help@stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting- > guide.html __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
[R] Off topic --- help in locating a source.
Apologies for the off-topic question; as usual I'm trying to draw upon the unparalleled knowledge and sagacity of the r-help list. Please reply off-list if you can help me out. A collaborator of mine found a formula we need, on sheets which he had photocopied out of a book, some years ago. He cannot remember which book (he's getting to be as senile and forgetful as I am, poor bloke!). He thinks it was (and it appears to have been) a large encylopedic tome devoted to extensive tables of formulae, integrals and series, and stuff like that. The formula in question is oo 1 1 1 SUM --- cos(k*x) = --- ln () 0 < x < 2*pi . k=1 k 2 2*(1 - cos(x)) (I.e. the right hand side is a function whose Fourier coefficients are 1/k, k > 0). Note that ``oo'' is my attempt to render the infinity symbol in ASCII. Does anyone know of a source where this formula may found/cited? (It doesn't *have* to be the same source from which my collaborator originally copied it!) It must be well-known/in lots of books, mustn't it? Said he, hopefully. Thanks for any assistance. cheers, Rolf Turner [EMAIL PROTECTED] __ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
