Tables Of Mellin Transforms
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Tables Of Mellin Transforms
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Author : F. Oberhettinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Tables Of Mellin 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 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 Mellin Transforms
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Author : Fritz Oberhettinger
language : de
Publisher:
Release Date : 1974
Tables Of Mellin 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 1974 with Mellin transform categories.
An Application And Generating Methods For Mellin Transforms
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Author : Bruce Rae Johnson
language : en
Publisher:
Release Date : 1964
An Application And Generating Methods For Mellin Transforms written by Bruce Rae Johnson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Transformations (Mathematics) categories.
Properties of Mellin transforms are applied to the summation of infinite series. A specific example of this application leads to the establishment of certain properties of a generalization of Lerch's zeta function. Nine powerful methods of generating new tables of Mellin transforms from existing tables of Mellin and other integral transforms are described and illustrated. A table of over 200 examples, which were derived from one of the above mentioned methods, is included.
Mellin Transform Method For Integral Evaluation
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Author : George Fikioris
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Mellin Transform Method For Integral Evaluation written by George Fikioris and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Technology & Engineering categories.
This book introduces the Mellin-transform method for the exact calculation of one-dimensional definite integrals, and illustrates the application if this method to electromagnetics problems. Once the basics have been mastered, one quickly realizes that the method is extremely powerful, often yielding closed-form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals. Yet, as opposed to other methods, the present method is very straightforward to apply; it usually requires laborious calculations, but little ingenuity. Two functions, the generalized hypergeometric function and the Meijer G-function, are very much related to the Mellin-transform method and arise frequently when the method is applied. Because these functions can be automatically handled by modern numerical routines, they are now much more useful than they were in the past. The Mellin-transform method and the two aforementioned functions are discussed first. Then the method is applied in three examples to obtain results, which, at least in the antenna/electromagnetics literature, are believed to be new. In the first example, a closed-form expression, as a generalized hypergeometric function, is obtained for the power radiated by a constant-current circular-loop antenna. The second example concerns the admittance of a 2-D slot antenna. In both these examples, the exact closed-form expressions are applied to improve upon existing formulas in standard antenna textbooks. In the third example, a very simple expression for an integral arising in recent, unpublished studies of unbounded, biaxially anisotropic media is derived. Additional examples are also briefly discussed.
Handbook Of Mellin Transforms
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Author : Anatolij Aleksandrovič Kilb̕as
language : en
Publisher:
Release Date : 2005-01
Handbook Of Mellin Transforms written by Anatolij Aleksandrovič Kilb̕as and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01 with categories.
This volume presents the tables of formulae for the evaluation of Mellin Transforms of elementary and special functions. The Handbook includes some formulae obtained by the authors and published for the first time. The tables are prefaced by a summary of notation for special functions and certain constants. The appendix contains some properties of the Mellin transform and applications. The results in tables are important for applications in different areas of mathematics, physics, mechanics, engineering, chemistry, biology and other applied sciences. The Handbook is a useful source of reference for graduate students and researchers.
Handbook Of Mellin Transforms
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Author : Yu. A. Brychkov
language : en
Publisher: CRC Press
Release Date : 2018-10-10
Handbook Of Mellin Transforms written by Yu. A. Brychkov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-10 with Mathematics categories.
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.
A Table Of Distributional Mellin Transforms
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Author : T. A. Loughlin
language : en
Publisher:
Release Date : 1965
A Table Of Distributional Mellin Transforms written by T. A. Loughlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Integral transforms categories.
A list of distributional Mellin transforms is derived. Singular distributions that are considered include delta functionals and pseudofunctions obtained from Hadamard's Finite Part. The ordinary distributionoons include algebraic and elementary transcendental functions. Proofs or derivations are provided for all results. (Author).
Handbook Of Mellin Transforms
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Author : Yu. A. Brychkov
language : en
Publisher: CRC Press
Release Date : 2018-10-10
Handbook Of Mellin Transforms written by Yu. A. Brychkov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-10 with Mathematics categories.
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.
A Table Of Distributional Mellin Transforms I
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Author : Timothy A. Loughlin
language : en
Publisher:
Release Date : 1965
A Table Of Distributional Mellin Transforms I written by Timothy A. Loughlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.
A list of distributional Mellin transforms is derived. Singular distributions that are considered include delta functionals and pseudofunctions obtained from Hadamard's Finite Part. The ordinary distributionoons include algebraic and elementary transcendental functions. Proofs or derivations are provided for all results. (Author).
Asymptotics And Mellin Barnes Integrals
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Author : R. B. Paris
language : en
Publisher: Cambridge University Press
Release Date : 2001-09-24
Asymptotics And Mellin Barnes Integrals written by R. B. Paris and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-24 with Mathematics categories.
Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.