Tables of Bessel Transforms, F. Oberhettinger

Автор: Dyke, P. P. G.
Название: An Introduction to Laplace transforms and Fourier series
ISBN: 1852330155 ISBN-13(EAN): 9781852330156
Издательство: Springer
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Описание: This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction.

Автор: F. Oberhettinger; L. Badii
Название: Tables of Laplace Transforms
ISBN: 3540063501 ISBN-13(EAN): 9783540063506
Издательство: Springer
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Описание: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Orthogonal Polynomials . 12 Legendre Functions . 13 Bessel Functions of Order Zero and Unity . 15 Modified Bessel Functions .

Автор: F. Oberhettinger
Название: Tables of Mellin Transforms
ISBN: 3540069429 ISBN-13(EAN): 9783540069423
Издательство: Springer
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Описание: This is partially due to the fact that if c(z) corresponding to a given q,(x) by (a) is known, then c(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. ) A list of major contributions conce~ning Mellin trans- forms is added at the end of the introduction. * . * * * . * . * * * * . * . * . * * * . * . * .

Автор: Fritz Oberhettinger
Название: Tables of Fourier Transforms and Fourier Transforms of Distributions
ISBN: 3540506306 ISBN-13(EAN): 9783540506300
Издательство: Springer
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Описание: 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 (C) ge(y) = J f(x)eixYdx Exponential Fourier Transform -00 Clearly, (A) and (B) are special cases of (C) 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 (C) 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), (C) 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 (C) are given.