Tables of Mellin Transforms

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Publisher : Springer Science & Business Media
ISBN 13 : 3642659756
Total Pages : 284 pages
Book Rating : 4.6/5 (426 download)

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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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Tables of Laplace Transforms

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Publisher : Springer Science & Business Media
ISBN 13 : 3642656455
Total Pages : 438 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Tables of Laplace Transforms by : F. Oberhettinger

Download or read book Tables of Laplace Transforms written by F. Oberhettinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 . . . . . . . . . . . . . . . . . . . . . . . .

Table of Integrals, Series, and Products

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Author :
Publisher : Elsevier
ISBN 13 : 0080471110
Total Pages : 1220 pages
Book Rating : 4.0/5 (84 download)

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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

Theoretical Aspects

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110681641
Total Pages : 334 pages
Book Rating : 4.1/5 (16 download)

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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.

Introduction to Bessel Functions

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Publisher : Courier Corporation
ISBN 13 : 0486152995
Total Pages : 148 pages
Book Rating : 4.4/5 (861 download)

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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.

Series of Bessel and Kummer-Type Functions

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Publisher : Springer
ISBN 13 : 3319743503
Total Pages : 218 pages
Book Rating : 4.3/5 (197 download)

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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.

CRC Standard Mathematical Tables and Formulae

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Publisher : CRC Press
ISBN 13 : 1420035347
Total Pages : 927 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis CRC Standard Mathematical Tables and Formulae by : Daniel Zwillinger

Download or read book CRC Standard Mathematical Tables and Formulae written by Daniel Zwillinger and published by CRC Press. This book was released on 2002-11-25 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt: A perennial bestseller, the 30th edition of CRC Standard Mathematical Tables and Formulae was the first "modern" edition of the handbook - adapted to be useful in the era of personal computers and powerful handheld devices. Now this version will quickly establish itself as the "user-friendly" edition. With a detailed table of contents and an extens

Bessel Functions and Their Applications

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Publisher : CRC Press
ISBN 13 : 9780203216927
Total Pages : 290 pages
Book Rating : 4.2/5 (169 download)

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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

Integral Transforms and Their Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 9780387953144
Total Pages : 398 pages
Book Rating : 4.9/5 (531 download)

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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.

Handbook of Formulas and Tables for Signal Processing

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Publisher : CRC Press
ISBN 13 : 9781420049701
Total Pages : 872 pages
Book Rating : 4.0/5 (497 download)

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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.

Integral and Discrete Transforms with Applications and Error Analysis

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Publisher : CRC Press
ISBN 13 : 1000147525
Total Pages : 852 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Integral and Discrete Transforms with Applications and Error Analysis by : Abdul Jerri

Download or read book Integral and Discrete Transforms with Applications and Error Analysis written by Abdul Jerri and published by CRC Press. This book was released on 2021-11-19 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.

Integral Transforms and Their Applications

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Publisher : CRC Press
ISBN 13 : 9780849394584
Total Pages : 480 pages
Book Rating : 4.3/5 (945 download)

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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.

Transforms and Applications Handbook

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Publisher : CRC Press
ISBN 13 : 1420066536
Total Pages : 911 pages
Book Rating : 4.4/5 (2 download)

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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.

Handbook of Linear Partial Differential Equations for Engineers and Scientists

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Publisher : CRC Press
ISBN 13 : 1466581492
Total Pages : 1623 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Handbook of Linear Partial Differential Equations for Engineers and Scientists by : Andrei D. Polyanin

Download or read book Handbook of Linear Partial Differential Equations for Engineers and Scientists written by Andrei D. Polyanin and published by CRC Press. This book was released on 2015-12-23 with total page 1623 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition contains nearly 4,000 linear partial differential equations (PDEs) with solutions as well as analytical, symbolic, and numerical methods for solving linear equations. First-, second-, third-, fourth-, and higher-order linear equations and systems of coupled equations are considered. Equations of parabolic, mixed, and other types are discussed. New linear equations, exact solutions, transformations, and methods are described. Formulas for effective construction of solutions are given. Boundary value and eigenvalue problems are addressed. Symbolic and numerical methods for solving PDEs with Maple, Mathematica, and MATLAB are explored.

Integrals and Series

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Publisher : Routledge
ISBN 13 : 135143795X
Total Pages : 644 pages
Book Rating : 4.3/5 (514 download)

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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.

Integrals and Series: Direct Laplace transforms

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Publisher : CRC Press
ISBN 13 : 9782881248375
Total Pages : 644 pages
Book Rating : 4.2/5 (483 download)

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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.

Table of Integrals, Series, and Products

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Publisher : Academic Press
ISBN 13 : 1483265641
Total Pages : 1207 pages
Book Rating : 4.4/5 (832 download)

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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.