Tables Of Bessel Transforms
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Tables Of Bessel Transforms
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Author : F. Oberhettinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Tables Of Bessel Transforms written by F. Oberhettinger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This material represents a collection of integral tra- forms involving Bessel (or related) functions as kernel. The following types of inversion formulas have been singled out. k I. g(y) = f (x) (xy) 2J (xy) dx J V 0 k I' . f (x) g (y) (xy) 2J (xy) dy J V 0 II. g(y) f(x) (XY)~K (xy)dx J v 0 c+ioo k 1 II'. f (x) = g (y) (xy) 2 [Iv (xy) + I_v(xy)]dy J 27fT c-ioo or also c+ioo k 1 II". f(x) = g (y) (xy) 2Iv (xy) dx J rri oo c-i k III. g(y) f(x) (xy) 2y (xy) dx + J v 0 k III' . f(x) g(y) (xy) "1lv (xy) dy J 0 k IV. g(y) f (x) (xy) "Kv (xy) dx J 0 k g(y) (xy) 2Y (xy)dy IV' - f(x) J v 0 V Preface V. g(y) f(X)Kix(y)dx J 0 -2 -1 sinh (7TX) V'. f(x) 27T x g(y)y Kix(y)dy J 0 21-~[r(~~+~-~v)r(~~+~+~v)]-1 VI. g(y) . J f (x) (xy) ~s (xy) dx o ~, v l-~ -1 VI' . f(x) 2 [r (~~+~-~v) r (~~+~+~v)] - - J -5 (xy)]dy g(y) (XY)~[S~, v(xy) ~, v 0 [xy)~]dX VII. g(y) f(x)\ ~ J 0 0 VII' - f(x) g(y) \ [(xy) lz]dy ~ f 0 0 with \ (z) o (For notations and definitions see the appendix of this book.) The transform VII is also known as the divisor transform.
Tables Of Laplace Transforms
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Author : F. Oberhettinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Tables Of Laplace Transforms written by F. Oberhettinger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This material represents a collection of integrals of the Laplace- and inverse Laplace Transform type. The usef- ness of this kind of information as a tool in various branches of Mathematics is firmly established. Previous publications include the contributions by A. Erdelyi and Roberts and Kaufmann (see References). Special consideration is given to results involving higher functions as integrand and it is believed that a substantial amount of them is presented here for the first time. Greek letters denote complex parameters within the given range of validity. Latin letters denote (unless otherwise stated) real positive parameters and a possible extension to complex values by analytic continuation will often pose no serious problem. The authors are indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manu script. Oregon State University Corvallis, Oregon Eastern Michigan University Ypsilanti, Michigan The Authors Contents Part I. Laplace Transforms In troduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 General Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 2 Algebraic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1. 3 Powers of Arbitrary Order. . . . . . . . . . . . . . . . . . . . . . . . 21 1. 4 Sectionally Rational- and Rows of Delta Functions 28 1. 5 Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1. 6 Logarithmic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 1. 7 Trigonometric Functions. . . . . . . . . . . . . . . . . . . . . . . . . . 54 1. 8 Inverse Trigonometric Functions. . . . . . . . . . . . . . . . . . 81 1. 9 Hyperbolic Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 1. 10 Inverse Hyperbolic Functions. . . . . . . . . . . . . . . . . . . . . 99 1. 11 Orthogonal Polynomials . . . . . . . •. . . . . . . . . . . . . . . . . . . 103 1. 12 Legendre Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 1. 13 Bessel Functions of Order Zero and Unity . . . . . . . . . 119 1. 14 Bessel Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 1. 15 Modified Bessel Functions . . . . . . . . . . . . . . . . . . . . . . . .
Tables Of Bessel Transforms
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Author : Fritz Oberhettinger
language : de
Publisher:
Release Date : 1972
Tables Of Bessel Transforms written by Fritz Oberhettinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Fourier Transforms Of Distributions And Their Inverses
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Author : Fritz Oberhettinger
language : en
Publisher: Academic Press
Release Date : 2014-07-03
Fourier Transforms Of Distributions And Their Inverses written by Fritz Oberhettinger and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Mathematics categories.
Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables contain Fourier transforms of absolutely continuous distribution functions, namely, even functions (including Legendre functions); functions vanishing identically for negative values of the argument (including arbitrary powers); and functions that do not belong to either of the above classes. The transform pairs are numbered consecutively and arranged systematically according to the analytical character of the frequency function. The next two tables give the inverse transforms of the functions listed in the first and third tables, respectively. This monograph will appeal to students and specialists in the fields of probability and mathematical statistics.
Tables Of Integral Transforms
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Author : Bateman Manuscript Project
language : en
Publisher:
Release Date : 1954
Tables Of Integral Transforms written by Bateman Manuscript Project and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Integral transforms categories.
Tables Of Integral Transforms
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Author : Bateman Manuscript Project
language : en
Publisher:
Release Date : 1954
Tables Of Integral Transforms written by Bateman Manuscript Project and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Integral transforms categories.
Table Of Integrals Series And Products
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Author : Daniel Zwillinger
language : en
Publisher: Elsevier
Release Date : 2007-02-23
Table Of Integrals Series And Products written by Daniel Zwillinger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-23 with Mathematics categories.
The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom. - Fully searchable CD that puts information at your fingertips included with text- Most up to date listing of integrals, series andproducts - Provides accuracy and efficiency in work
Tables Of Integral Transforms
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Author : Bateman Manuscript Project
language : en
Publisher:
Release Date : 1954
Tables Of Integral Transforms written by Bateman Manuscript Project and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with Integral transforms categories.
Tables Of Laplace Heaviside Fourier And Z Transforms
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Author : Martin Healey
language : en
Publisher:
Release Date : 1967
Tables Of Laplace Heaviside Fourier And Z Transforms written by Martin Healey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Calculus, Operational categories.
Table Of Modified Bessel Functions
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Author : Henry E. Fettis
language : en
Publisher:
Release Date : 1969
Table Of Modified Bessel Functions written by Henry E. Fettis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Bessel functions categories.