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
rolf at math.unb.ca
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: rvaradhan at jhmi.edu --------------------------------------------------------------------------> -----Original Message----- > From: r-help-bounces at stat.math.ethz.ch [mailto:r-help- > bounces at stat.math.ethz.ch] On Behalf Of Rolf Turner > Sent: Wednesday, May 17, 2006 3:27 PM > To: r-help at 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 > rolf at math.unb.ca > > ______________________________________________ > R-help at 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
If a web site is suffiicent then: http://functions.wolfram.com/ElementaryFunctions/Cos/23/02/ On 5/17/06, Rolf Turner <rolf at math.unb.ca> 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 > rolf at math.unb.ca > > ______________________________________________ > R-help at 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 >
Augusto.Sanabria at ga.gov.au
2006-May-18 23:26 UTC
[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: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Rolf Turner
Sent: Thursday, 18 May 2006 5:27 AM
To: r-help at 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
rolf at math.unb.ca
______________________________________________
R-help at 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