Fred wrote: << . . . The "delta" is not a Kronecker delta, but an infinite spike whose integral is nonzero (here pi): this is an example of a "distribution", a generalisation of the classical notion of "function" which permits such limiting cases to be discussed compactly. . . .
Thanks. (A slip of the fingers; I meant Dirac delta. Yes, indeed, a linear functional on the vector space of functions, given by delta(f) = f(0). I'm only half as confused as I seem to be.) I'm almost sure you're right that the author is "by convention" setting 1/(1-exp(iw)) to 0 where w = 2k*pi, and then adding explicitly the "singular part", a periodic delta function. --------------------------------------------------------------------- I'm thinking, f(w) = 1/(1-exp(iw)) = -2i exp(-iw/2) / sin(w). So maybe somehow integral_a^b(f(w)) = (1/2)*(2 pi*i) * (Res(f(w)) at w=0) can be used to express the "singular part" of f(w) ??? --Dan