Tables of Fourier Transforms and Fourier Transforms of Distributions

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These tables represent a new, revised and enlarged version of the previously published book by this author, entitled Tabellen zur Fourier Transformation (Springer Verlag 1957). Known errors have been correc- ted, apart from the addition of a considerable number of new results, which involve almost exclusively higher functions. Again, the follow- ing tables contain a collection of integrals of the form J f(x)cos(xy)dx Fourier Cosine Transform (Al o (B) J f(x)sin(xy)dx Fourier Sine Transform o © ge(y) = J f(x)eixYdx Exponential Fourier Transform -00 Clearly, (A) and (B) are special cases of © if f(x) is respec- tively an even or an odd function. The transform parameter y in (A) and (B) is assumed to be positive, while in © negative values are also included. A possible analytic continuation to complex parameters y* should present no difficulties. In some cases the result function g(y) is given over a partial range of y only. This means that g(y) for the remaining part of y cannot be given in a reasonably simple form. Under certain conditions the following inversion formulas for (A), (B), © hold: (A’ ) f(x) = 2 J g (y)cos(xy)dy 11 0 c 2 J (B’) f (x) gs(y)sin(xy)dy 11 0 -1 00 -ix (C’ ) f(x) = (211) J ge(y)e Ydy In the following parts I, II, III tables for the transforms (A), (B) and © are given.