[R] Off topic --- help in locating a source.

Augusto.Sanabria at ga.gov.au
Thu, 18 May 2006 23:26:08 -0000

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

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