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Tables Of Bessel Transforms
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Book Synopsis Tables of Bessel Transforms by : F. Oberhettinger
Download or read book Tables of Bessel Transforms written by F. Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tables of Mellin Transforms by : F. Oberhettinger
Download or read book Tables of Mellin Transforms written by F. Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains tables of integrals of the Mellin transform type z-l J (a) 1> (z) q,(x)x dx o t Since the substitution x = e- transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided Laplace transform. The use of the Mellin transform in various problems in mathematical analysis is well established. Parti cularly widespread and effective is its application to problems arising in analytic number theory. This is partially due to the fact that if ¢(z) corresponding to a given q,(x) by (a) is known, then ¢(z) belonging to xaq,(x) or more general to P xaq,(x ) (p real) is likewise known. (See particularly the rules in sections 1. 1 and 2. 1 of this book. ) A list of major contributions conce~ning Mellin trans forms is added at the end of the introduction. Latin letters (unless otherwise stated) denote real positive numbers while Greek letters denote complex parameters within the given range of validity. The author is indebted to Mrs. Jolan Eross for her tireless effort and patience while typing this manuscript. Oregon State University Corvallis, Oregon May 1974 Fritz Oberhettinger Contents Part I. Mellin Transforms Introduction. . . • . • • • . • . . . . . . . . . . . . • • • • . . . • . • . . • • • . • . 1 Some Applications of the Mellin Transform Analysis. ••. •••. . . •. •. . . . •• . • . . . . . . ••. . . . . •• 6 1. 1 General Formulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1. 2 Algebraic Functions and Powers of Arbitrary Order . . . 13 1. 3 Exponential Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Book Synopsis Table of Integrals, Series, and Products by : Daniel Zwillinger
Download or read book Table of Integrals, Series, and Products written by Daniel Zwillinger and published by Elsevier. This book was released on 2007-02-23 with total page 1220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Introduction to Bessel Functions by : Frank Bowman
Download or read book Introduction to Bessel Functions written by Frank Bowman and published by Courier Corporation. This book was released on 2012-04-27 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained text, useful for classroom or independent study, covers Bessel functions of zero order, modified Bessel functions, definite integrals, asymptotic expansions, and Bessel functions of any real order. 226 problems.
Book Synopsis Theoretical Aspects by : Alexander Apelblat
Download or read book Theoretical Aspects written by Alexander Apelblat and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-04-20 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bessel functions have the peculiarity of being functions of two independent variables: argument and order. They have been studied extensively because of their countless applications, but the vast majority of available literature is devoted to the case of fixed order, variable argument. This two-volume work explores the opposite case. This volume focuses on properties of the functions and mathematical operations with respect to the order.
Book Synopsis Series of Bessel and Kummer-Type Functions by : Árpád Baricz
Download or read book Series of Bessel and Kummer-Type Functions written by Árpád Baricz and published by Springer. This book was released on 2018-03-24 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.
Book Synopsis Bessel Functions and Their Applications by : B G Korenev
Download or read book Bessel Functions and Their Applications written by B G Korenev and published by CRC Press. This book was released on 2002-07-25 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bessel functions are associated with a wide range of problems in important areas of mathematical physics. Bessel function theory is applied to problems of acoustics, radio physics, hydrodynamics, and atomic and nuclear physics. Bessel Functions and Their Applications consists of two parts. In Part One, the author presents a clear and rigorous intro
Book Synopsis Integrals and Series: Direct Laplace transforms by : Anatoliĭ Platonovich Prudnikov
Download or read book Integrals and Series: Direct Laplace transforms written by Anatoliĭ Platonovich Prudnikov and published by CRC Press. This book was released on 1986 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volumes 4 and 5 of the extensive series Integrals and Series are devoted to tables of LaplaceTransforms. In these companion volumes the authors have collected data scatteredthroughout the literature, and have augmented this material with many unpublished resultsobtained in their own research.Volume 4 contains tables of direct Laplace transforms, a number of which are expressed interms of the Meijer G-function. When combined with the table of special cases, theseformulas can be used to obtain Laplace transforms of numerous elementary and specialfunctions of mathematical physics.Volume 5 offers tables of inversion formulas for the Laplace transformation and includestables of factorization and inversion of various integral transforms.
Book Synopsis Integral Transforms and Their Applications by : Lokenath Debnath
Download or read book Integral Transforms and Their Applications written by Lokenath Debnath and published by CRC Press. This book was released on 1995-07-03 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Transforms and Their Applications, provides a systematic , comprehensive review of the properties of integral transforms and their applications to the solution of boundary and initial value problems. Over 750 worked examples, exercises, and applications illustrate how transform methods can be used to solve problems in applied mathematics, mathematical physics, and engineering. The specific applications discussed include problems in differential, integral, and difference equations; electric circuits and networks; vibrations and wave propagation; heat conduction; fractional derivatives and fractional integrals; dynamical systems; signal processing; quantum mechanics; atmosphere and ocean dynamics; physical chemistry; mathematical biology; and probability and statistics. Integral Transforms and Their Applications includes broad coverage the standard material on integral transforms and their applications, along with modern applications and examples of transform methods. It is both an ideal textbook for students and a sound reference for professionals interested in advanced study and research in the field.
Book Synopsis Integrals and Series by : A.B Prudnikov
Download or read book Integrals and Series written by A.B Prudnikov and published by Routledge. This book was released on 2018-05-02 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volumes 4 and 5 of the extensive series Integrals and Series are devoted to tables of LaplaceTransforms. In these companion volumes the authors have collected data scatteredthroughout the literature, and have augmented this material with many unpublished resultsobtained in their own research.Volume 4 contains tables of direct Laplace transforms, a number of which are expressed interms of the Meijer G-function. When combined with the table of special cases, theseformulas can be used to obtain Laplace transforms of numerous elementary and specialfunctions of mathematical physics.Volume 5 offers tables of inversion formulas for the Laplace transformation and includestables of factorization and inversion of various integral transforms.
Book Synopsis Integral Transforms and Their Applications by : Brian Davies
Download or read book Integral Transforms and Their Applications written by Brian Davies and published by Springer Science & Business Media. This book was released on 2002-01-02 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a substantially updated, extended and reorganized third edition of an introductory text on the use of integral transforms. Chapter I is largely new, covering introductory aspects of complex variable theory. Emphasis is on the development of techniques and the connection between properties of transforms and the kind of problems for which they provide tools. Around 400 problems are accompanied in the text. It will be useful for graduate students and researchers working in mathematics and physics.
Book Synopsis Table of Integrals, Series, and Products by : I. S. Gradshteyn
Download or read book Table of Integrals, Series, and Products written by I. S. Gradshteyn and published by Academic Press. This book was released on 2014-05-10 with total page 1207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.
Book Synopsis Tables of Integral Transforms by : Bateman Manuscript Project
Download or read book Tables of Integral Transforms written by Bateman Manuscript Project and published by . This book was released on 1954 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Transforms and Applications Handbook by : Alexander D. Poularikas
Download or read book Transforms and Applications Handbook written by Alexander D. Poularikas and published by CRC Press. This book was released on 2018-09-03 with total page 911 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.
Book Synopsis Integral Transforms and their Applications by : B. Davies
Download or read book Integral Transforms and their Applications written by B. Davies and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: In preparing this second edition I have restricted myself to making small corrections and changes to the first edition. Two chapters have had extensive changes made. First, the material of Sections 14.1 and 14.2 has been rewritten to make explicit reference to the book of Bleistein and Handelsman, which appeared after the original Chapter 14 had been written. Second, Chapter 21, on numerical methods, has been rewritten to take account of comparative work which was done by the author and Brian Martin, and published as a review paper. The material for all of these chapters was in fact, prepared for a transla tion of the book. Considerable thought has been given to a much more com prehensive revision and expansion of the book. In particular, there have been spectacular advances in the solution of some non-linear problems using isospectra1 methods, which may be re garded as a generalization of the Fourier transform. However, the subject is a large one, and even a modest introduction would have added substantially to the book. Moreover, the recent book by Dodd et al. is at a similar level to the present volume. Similarly, I have refrained from expanding the chapter on num erical methods into a complete new part of the book, since a specialized monograph on numerical methods is in preparation in collaboration with a colleague.
Book Synopsis Handbook of Formulas and Tables for Signal Processing by : Alexander D. Poularikas
Download or read book Handbook of Formulas and Tables for Signal Processing written by Alexander D. Poularikas and published by CRC Press. This book was released on 1998-09-29 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: Signal processing is a broad and timeless area. The term "signal" includes audio, video, speech, image, communication, geophysical, sonar, radar, medical, and more. Signal processing applies to the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals. Handbook of Formulas and Tables for Signal Processing a must-have reference for all engineering professionals involved in signal and image processing. Collecting the most useful formulas and tables - such as integral tables, formulas of algebra, formulas of trigonometry - the text includes: Material for the deterministic and statistical signal processing areas Examples explaining the use of the given formula Numerous definitions Many figures that have been added to special chapters Handbook of Formulas and Tables for Signal Processing brings together - in one textbook - all the equations necessary for signal and image processing for professionals transforming anything from a physical to a manipulated form, creating a new standard for any person starting a future in the broad, extensive area of research.
