Handbook of Mellin Transforms

Handbook of Mellin Transforms
Author: Yu. A. Brychkov
Publisher: CRC Press
Total Pages: 788
Release: 2018-10-10
Genre: Mathematics
ISBN: 0429784430

The Mellin transformation is widely used in various problems of pure and applied mathematics, in particular, in the theory of differential and integral equations and the theory of Dirichlet series. It is found in extensive applications in mathematical physics, number theory, mathematical statistics, theory of asymptotic expansions, and especially, in the theory of special functions and integral transformations. It is essentially used in algorithms of integration in computer algebra systems. Since the majority of integrals encountered in applications can be reduced to the form of the corresponding Mellin transforms with specific parameters, this handbook can also be used for definite and indefinite integrals. By changes in variables, the Mellin transform can be turned into the Fourier and Laplace transforms. The appendices contain formulas of connection with other integral transformations, and an algorithm for determining regions of convergence of integrals. The Handbook of Mellin Transforms will be of interest and useful to all researchers and engineers who use mathematical methods. It will become the main source of formulas of Mellin transforms, as well as indefinite and definite integrals.

Transforms and Applications Handbook

Transforms and Applications Handbook
Author: Alexander D. Poularikas
Publisher: CRC Press
Total Pages: 911
Release: 2018-09-03
Genre: Mathematics
ISBN: 1420066536

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 Function and Generalized Function Transformations

Handbook of Function and Generalized Function Transformations
Author: Ahmed I. Zayed
Publisher: CRC Press
Total Pages: 684
Release: 1996-05-15
Genre: Mathematics
ISBN: 9780849378515

Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems. The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included. The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations. It is organized for convenient reference, with chapters broken down into the following sections:

Handbook of Integral Equations

Handbook of Integral Equations
Author: Andrei D. Polyanin
Publisher: CRC Press
Total Pages: 1143
Release: 2008-02-12
Genre: Mathematics
ISBN: 0203881052

Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa

Tables of Mellin Transforms

Tables of Mellin Transforms
Author: F. Oberhettinger
Publisher: Springer Science & Business Media
Total Pages: 284
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642659756

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

Handbook of Formulas and Tables for Signal Processing

Handbook of Formulas and Tables for Signal Processing
Author: Alexander D. Poularikas
Publisher: CRC Press
Total Pages: 872
Release: 1998-09-29
Genre: Technology & Engineering
ISBN: 9781420049701

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.

Table of Integrals, Series, and Products

Table of Integrals, Series, and Products
Author: I. S. Gradshteyn
Publisher: Academic Press
Total Pages: 1207
Release: 2014-05-10
Genre: Mathematics
ISBN: 1483265641

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.

Handbook of Function and Generalized Function Transformations

Handbook of Function and Generalized Function Transformations
Author: Ahmed I. Zayed
Publisher: CRC Press
Total Pages: 672
Release: 2019-08-21
Genre: Mathematics
ISBN: 0429610912

Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems. The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included. The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations. It is organized for convenient reference, with chapters broken down into the following sections: