Talk:Sigma approximation

Hi.

I've just edited the page to correct an error in the argument of the sinc function, and I thought I'd give some background info. The error appears in [Acton, F. S. Numerical Methods That Work, 2nd printing. Washington, DC: Math. Assoc. Amer., p. 228, 1990] and hence has propagated on the web. However the correct version appears in e.g. [Hamming, R. W. "Lanczos' Factors" and "The Factors in the General Case." §32.6 and 32.7 in Numerical Methods for Scientists and Engineers, 2nd ed. New York: Dover, pp. 534-536, 1986] as is also stated at

http://mathworld.wolfram.com/LanczosSigmaFactor.html.

I've also edited the mathematical expression to explicitly show that the sigma approximation can be used unchanged from the given form in the case of an arbitrary period T. This can be verified by reworking the proof on p. 535 of Hamming (1986) with a generalized period.