Asymptotics and Special Functions

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Publisher : Academic Press
ISBN 13 : 148326744X
Total Pages : 589 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Asymptotics and Special Functions by : F. W. J. Olver

Download or read book Asymptotics and Special Functions written by F. W. J. Olver and published by Academic Press. This book was released on 2014-05-10 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.

Introduction to Asymptotics and Special Functions

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Publisher : Academic Press
ISBN 13 : 1483267083
Total Pages : 312 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Introduction to Asymptotics and Special Functions by : F. W. J. Olver

Download or read book Introduction to Asymptotics and Special Functions written by F. W. J. Olver and published by Academic Press. This book was released on 2014-05-10 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Asymptotics and Special Functions is a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable are discussed, along with contour integrals and differential equations with regular and irregular singularities. The Liouville-Green approximation is also considered. Comprised of seven chapters, this volume begins with an overview of the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on integrals of a real variable. Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions. A chapter devoted to the Liouville-Green approximation tackles asymptotic properties with respect to parameters and to the independent variable, eigenvalue problems, and theorems on singular integral equations. This monograph is intended for students needing only an introductory course to asymptotics and special functions.

Asymptotics and Special Functions

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Author :
Publisher : CRC Press
ISBN 13 : 1439864543
Total Pages : 591 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Asymptotics and Special Functions by : Frank Olver

Download or read book Asymptotics and Special Functions written by Frank Olver and published by CRC Press. This book was released on 1997-01-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.

Asymptotics and Special Functions [By] F.W.J. Olver

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Publisher :
ISBN 13 :
Total Pages : 572 pages
Book Rating : 4.:/5 (1 download)

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Book Synopsis Asymptotics and Special Functions [By] F.W.J. Olver by : Frank W. J. Olver

Download or read book Asymptotics and Special Functions [By] F.W.J. Olver written by Frank W. J. Olver and published by . This book was released on 1974 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Asymptotics and Special Functions

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Publisher :
ISBN 13 :
Total Pages : 588 pages
Book Rating : 4.:/5 (23 download)

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Book Synopsis Asymptotics and Special Functions by : Frank W. J. Olver

Download or read book Asymptotics and Special Functions written by Frank W. J. Olver and published by . This book was released on 1973 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Orthogonal Polynomials and Special Functions

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Publisher : Springer
ISBN 13 : 3540449450
Total Pages : 259 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Orthogonal Polynomials and Special Functions by : Erik Koelink

Download or read book Orthogonal Polynomials and Special Functions written by Erik Koelink and published by Springer. This book was released on 2003-07-03 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The set of lectures from the Summer School held in Leuven in 2002 provide an up-to-date account of recent developments in orthogonal polynomials and special functions, in particular for algorithms for computer algebra packages, 3nj-symbols in representation theory of Lie groups, enumeration, multivariable special functions and Dunkl operators, asymptotics via the Riemann-Hilbert method, exponential asymptotics and the Stokes phenomenon. Thenbsp;volume aims at graduate students and post-docs working in the field of orthogonal polynomials and special functions, and in related fields interacting with orthogonal polynomials, such as combinatorics, computer algebra, asymptotics, representation theory, harmonic analysis, differential equations, physics. The lectures are self-contained requiring onlynbsp;a basic knowledge of analysis and algebra, and each includes many exercises.

NIST Handbook of Mathematical Functions Hardback and CD-ROM

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Publisher : Cambridge University Press
ISBN 13 : 0521192250
Total Pages : 968 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis NIST Handbook of Mathematical Functions Hardback and CD-ROM by : Frank W. J. Olver

Download or read book NIST Handbook of Mathematical Functions Hardback and CD-ROM written by Frank W. J. Olver and published by Cambridge University Press. This book was released on 2010-05-17 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.

Asymptotic and Computational Analysis

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Publisher : CRC Press
ISBN 13 : 1000154130
Total Pages : 782 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Asymptotic and Computational Analysis by : R. Wong

Download or read book Asymptotic and Computational Analysis written by R. Wong and published by CRC Press. This book was released on 2020-12-17 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers presented at the International Symposium on Asymptotic and Computational Analysis, held June 1989, Winnipeg, Man., sponsored by the Dept. of Applied Mathematics, University of Manitoba and the Canadian Applied Mathematics Society.

Asymptotic and Computational Analysis

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Publisher : CRC Press
ISBN 13 : 1000111040
Total Pages : 776 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Asymptotic and Computational Analysis by : R. Wong

Download or read book Asymptotic and Computational Analysis written by R. Wong and published by CRC Press. This book was released on 2020-12-17 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers presented at the International Symposium on Asymptotic and Computational Analysis, held June 1989, Winnipeg, Man., sponsored by the Dept. of Applied Mathematics, University of Manitoba and the Canadian Applied Mathematics Society.

Modern Trends in Constructive Function Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 1470425343
Total Pages : 312 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Modern Trends in Constructive Function Theory by : E. B. Saff

Download or read book Modern Trends in Constructive Function Theory written by E. B. Saff and published by American Mathematical Soc.. This book was released on 2016-03-31 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the conference Constructive Functions 2014, held in May 2014. The papers in this volume include results on polynomial approximation, rational approximation, Log-optimal configurations on the sphere, random continued fractions, ratio asymptotics for multiple orthogonal polynomials, the bivariate trigonometric moment problem, and random polynomials.

Selected Asymptotic Methods with Applications to Electromagnetics and Antennas

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Publisher : Springer Nature
ISBN 13 : 3031017161
Total Pages : 187 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Selected Asymptotic Methods with Applications to Electromagnetics and Antennas by : George Fikioris

Download or read book Selected Asymptotic Methods with Applications to Electromagnetics and Antennas written by George Fikioris and published by Springer Nature. This book was released on 2022-06-01 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals.

Asymptotic Approximations of Integrals

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Publisher : Academic Press
ISBN 13 : 1483220710
Total Pages : 561 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Asymptotic Approximations of Integrals by : R. Wong

Download or read book Asymptotic Approximations of Integrals written by R. Wong and published by Academic Press. This book was released on 2014-05-10 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.

Differential Equations & Asymptotic Theory in Mathematical Physics

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Publisher : World Scientific
ISBN 13 : 9812560556
Total Pages : 389 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Differential Equations & Asymptotic Theory in Mathematical Physics by : Zhen Hua

Download or read book Differential Equations & Asymptotic Theory in Mathematical Physics written by Zhen Hua and published by World Scientific. This book was released on 2004 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings? (ISTP? / ISI Proceedings)? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences

Introduction to asymptotic and special functions

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Publisher :
ISBN 13 :
Total Pages : 297 pages
Book Rating : 4.:/5 (17 download)

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Book Synopsis Introduction to asymptotic and special functions by : F. W. Olver

Download or read book Introduction to asymptotic and special functions written by F. W. Olver and published by . This book was released on 1974 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lecture Notes On Applied Analysis

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Publisher : World Scientific Publishing Company
ISBN 13 : 9813107669
Total Pages : 303 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Lecture Notes On Applied Analysis by : Roderick S C Wong

Download or read book Lecture Notes On Applied Analysis written by Roderick S C Wong and published by World Scientific Publishing Company. This book was released on 2010-01-18 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are several subjects in analysis that are frequently used in applied mathematics, theoretical physics and engineering sciences, such as complex variable, ordinary differential equations, special functions, asymptotic methods, integral transforms and distribution theory. However, for graduate students or upper-level undergraduate students who are not going to specialize in these areas, there is no need for them to study these subjects in great depth. Instead, it would probably be more beneficial for them to have an introduction to these topics so that when the need arises, they know what approach to take. With this in mind, this set of lecture notes has been written for a one-semester course. Sufficient details have also been included to make it sufficiently adaptable for self-study. There are in total six chapters with each covering only a few topics. Furthermore, the chapters are all self-contained. The prerequisites for the readers of this book are advanced calculus, a first course in ordinary differential equations and elementary complex variable.

Ship Hydrodynamics, Water Waves, and Asymptotics

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Author :
Publisher : World Scientific
ISBN 13 : 9789810219505
Total Pages : 452 pages
Book Rating : 4.2/5 (195 download)

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Book Synopsis Ship Hydrodynamics, Water Waves, and Asymptotics by : Fritz Ursell

Download or read book Ship Hydrodynamics, Water Waves, and Asymptotics written by Fritz Ursell and published by World Scientific. This book was released on 1994 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Springer Handbook of Atomic, Molecular, and Optical Physics

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Publisher : Springer Nature
ISBN 13 : 3030738930
Total Pages : 1436 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Springer Handbook of Atomic, Molecular, and Optical Physics by : Gordon W. F. Drake

Download or read book Springer Handbook of Atomic, Molecular, and Optical Physics written by Gordon W. F. Drake and published by Springer Nature. This book was released on 2023-02-09 with total page 1436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprises a comprehensive reference source that unifies the entire fields of atomic molecular and optical (AMO) physics, assembling the principal ideas, techniques and results of the field. 92 chapters written by about 120 authors present the principal ideas, techniques and results of the field, together with a guide to the primary research literature (carefully edited to ensure a uniform coverage and style, with extensive cross-references). Along with a summary of key ideas, techniques, and results, many chapters offer diagrams of apparatus, graphs, and tables of data. From atomic spectroscopy to applications in comets, one finds contributions from over 100 authors, all leaders in their respective disciplines. Substantially updated and expanded since the original 1996 edition, it now contains several entirely new chapters covering current areas of great research interest that barely existed in 1996, such as Bose-Einstein condensation, quantum information, and cosmological variations of the fundamental constants. A fully-searchable CD- ROM version of the contents accompanies the handbook.