Abramowitz, M. and Stegun, I. A. Handbook of Mathematical Functions. Dover, New York. 1965

Abramowitz, M. and Stegun, I. A. A more up-to-date version of Jahnke & Emde, below

Bracewell, R. N. The Fourier Transform and its Applications. McGraw-Hill, New York. 1965

Bracewell, R. N. This is one of the two most popular books on the subject. Similar in scope to this book, but more thorough and comprehensive

Brigham, E. O. The Fast Fourier Transform. Prentice Hall, New York. 1974

Brigham, E. O. The standard work on digital Fourier transforms and their implementation by various kinds of FFT programs

Champeney, D. C. Fourier Transforms and Their Physical Applications. Academic Press, London and New York. 1973

Champeney, D. C. Like Bracewell, one of the two most popular books on practical Fourier tranforming. Covers similar ground, but with some differences

Champeney, D. C. A Handbook of Fourier Theorems. Cambridge University Press. 1987

Herman, Gabor T. Image Reconstruction From Projections. Academic Press, London and New York. 1980

Herman, Gabor T. Includes details of Fourier methods (among others) for computerized tomography, including theory and applications

Jahnke, E and Emde, F. Tables of Functions with Formulae and Curves. Dover, New York. 1943

Jahnke, E and Emde, F. The classic work on the functions of mathematical physics, with diagrams, charts and tables, of Bessel functions, Legendre polynomials, spherical harmonics etc

Körner, T. W. Fourier Analysis. Cambridge University Press. 1988

Körner, T. W. One of the more thorough and entertaining works on analytic Fourier theory, but plenty of physical applications: expensive, but firmly recommended for serious students

Titchmarsh, E. C. An Introduction to the theory of Fourier Integrals. Clarendon Press, Oxford. 1962

Titchmarsh, E. C. The theorists' standard work on Fourier theory. Unnecessarily difficult for ordinary mortals, but needs consulting occasionally

Watson, G. N. A Treatise of the Theory of Bessel Functions, Cambridge University Press. 1962

Watson, G. N. Another great theoretical classic: chiefly for consultation by people who have equations they can't solve, and which seem likely to involve Bessel functions

Whittaker, J. M. Interpolary Function Theory, Cambridge University Press. 1935

Whittaker, J. M. A slim volume dealing with (among other things) the sampling theorem and problems of interpolating points between samples of band-limited curves