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

Rolf Turner
Wed, 17 May 2006 19:27:16 -0000

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