Author: Ian Naismith Sneddon

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### Special functions of mathematical physics and chemistry

### Special Functions

The author provides an introduction to the classical well-known special functions which play a role in mathematical physics, especially in boundary value problems. Written for students and researchers in mathematics, physics, and engineering who encounter special functions in their work and for whom the results are too scattered in the general literature. Includes scores of exercises and notations at the end of every chapter.

### Special Functions of Mathematical Physics

With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan tum mechanics. We have not attempted to provide the most extensive collec tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics. For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem (§3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (§§12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical or thogonal polynomials of a discrete variable on both uniform and nonuniform lattices has been given such a coherent presentation, together with its various applications in physics.

### Mathematics for Chemistry and Physics

Chemistry and physics share a common mathematical foundation. From elementary calculus to vector analysis and group theory, Mathematics for Chemistry and Physics aims to provide a comprehensive reference for students and researchers pursuing these scientific fields. The book is based on the authors many classroom experience. Designed as a reference text, Mathematics for Chemistry and Physics will prove beneficial for students at all university levels in chemistry, physics, applied mathematics, and theoretical biology. Although this book is not computer-based, many references to current applications are included, providing the background to what goes on "behind the screen" in computer experiments.

### Special Functions for Scientists and Engineers

Physics, chemistry, and engineering undergraduates will benefit from this straightforward guide to special functions. Its topics possess wide applications in quantum mechanics, electrical engineering, and many other fields. 1968 edition. Includes 25 figures.

### Analysis And Mathematical Physics

This is a concise reference book on analysis and mathematical physics, leading readers from a foundation to advanced level understanding of the topic. This is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as distributions, Fourier transforms and microlocal analysis, C* Algebras, value distribution of meromorphic functions, noncommutative differential geometry, differential geometry and mathematical physics, mathematical problems of general relativity, and special functions of mathematical physics. Analysis and Mathematical Physics is the sixth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

### Elements Of Ordinary Differential Equations And Special Functions

Ordinary Differential Equations And Special Functions Form A Central Part In Many Branches Of Physics And Engineering. A Large Number Of Books Already Exist In These Areas And Informations Are Therefore Available In A Scattered Form. The Present Book Tries To Bring Out Some Of The Most Important Concepts Associated With Linear Ordinary Differential Equations And The Special Functions Of Frequent Occurrence, In A Rather Elementary Form.The Methods Of Obtaining Series Solution Of Second Order Linear Ordinary Differential Equations Near An Ordinary Point As Well As Near A Regular Singular Point Have Been Explained In An Elegant Manner And, As Applications Of These Methods, The Special Functions Of Hermite And Bessel Have Been Dealt With.The Special Functions Of Legendre And Laguerre Have Also Been Discussed Briefly. An Appendix Is Prepared To Deal With Other Special Functions Such As The Beta Function, The Gamma Function, The Hypergeometric Functions And The Chebyshev Polynomials In A Short Form.The Topics Involving The Existence Theory And The Eigenvalue Problems Have Also Been Discussed In The Book To Create Motivation For Further Studies In The Subject.Each Chapter Is Supplemented With A Number Of Worked Out Examples As Well As A Number Of Problems To Be Handled For Better Understanding Of The Subject. R Contains A List Of Sixteen Important Books Forming The Bibliography.In This Second Edition The Text Has Been Thoroughly Revised.

### Special Matrices of Mathematical Physics

This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas concerning Lie algebra invariants, differential geometry and real gases, and their matrices are instrumental in the study of chaotic mappings. Contents: Basics: Some Fundamental Notions; Stochastic Matrices: Evolving Systems; Markov Chains; Glass Transition; The Kerner Model; Formal Developments; Equilibrium, Dissipation and Ergodicity; Circulant Matrices: Prelude; Definition and Main Properties; Discrete Quantum Mechanics; Quantum Symplectic Structure; Bell Matrices: An Organizing Tool; Bell Polynomials; Determinants and Traces; Projectors and Iterates; Gases: Real and Ideal. Readership: Mathematical physicists, statistical physicists and researchers in the field of combinatorics and graph theory.

### A Guide to Mathematical Methods for Physicists

Mathematics plays a fundamental role in the formulation of physical theories. This textbook provides a self-contained and rigorous presentation of the main mathematical tools needed in many fields of Physics, both classical and quantum. It covers topics treated in mathematics courses for final-year undergraduate and graduate physics programmes, including complex function: distributions, Fourier analysis, linear operators, Hilbert spaces and eigenvalue problems. The different topics are organised into two main parts — complex analysis and vector spaces — in order to stress how seemingly different mathematical tools, for instance the Fourier transform, eigenvalue problems or special functions, are all deeply interconnected. Also contained within each chapter are fully worked examples, problems and detailed solutions. A companion volume covering more advanced topics that enlarge and deepen those treated here is also available. Contents:Complex Analysis:Holomorphic FunctionsIntegrationTaylor and Laurent SeriesResiduesFunctional Spaces:Vector SpacesSpaces of FunctionsDistributionsFourier AnalysisLinear Operators in Hilbert Spaces I: The Finite-Dimensional CaseLinear Operators in Hilbert Spaces II: The Infinite-Dimensional CaseAppendices:Complex Numbers, Series and IntegralsSolutions of the Exercises Readership: Students of undergraduate mathematics and postgraduate students of physics or engineering.

### Special Functions & Their Applications

Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.

### Special Functions and Orthogonal Polynomials

(308 Pages). This book is written to provide an easy to follow study on the subject of Special Functions and Orthogonal Polynomials. It is written in such a way that it can be used as a self study text. Basic knowledge of calculus and differential equations is needed. The book is intended to help students in engineering, physics and applied sciences understand various aspects of Special Functions and Orthogonal Polynomials that very often occur in engineering, physics, mathematics and applied sciences. The book is organized in chapters that are in a sense self contained. Chapter 1 deals with series solutions of Differential Equations. Gamma and Beta functions are studied in Chapter 2 together with other functions that are defined by integrals. Legendre Polynomials and Functions are studied in Chapter 3. Chapters 4 and 5 deal with Hermite, Laguerre and other Orthogonal Polynomials. A detailed treatise of Bessel Function in given in Chapter 6.

### Special Functions

### Periods and Special Functions in Transcendence

This book gives an introduction to some central results in transcendental number theory with application to periods and special values of modular and hypergeometric functions. It also includes related results on CalabiYau manifolds. Most of the material is based on the author's own research and appears for the first time in book form. It is presented with minimal of technical language and no background in number theory is needed. In addition, except the last chapter, all chapters include exercises suitable for graduate students.

### Group Theory in Physics

An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet. Request Inspection Copy

### Mathematics of Physics and Engineering

Aimed at scientists and engineers, this book is an exciting intellectual journey through the mathematical worlds of Euclid, Newton, Maxwell, Einstein, and Schrodinger-Dirac. While similar books present the required mathematics in a piecemeal manner with tangential references to the relevant physics and engineering, this textbook serves the interdisciplinary needs of engineers, scientists and applied mathematicians by unifying the mathematics and physics into a single systematic body of knowledge but preserving the rigorous logical development of the mathematics. The authors take an unconventional approach by integrating the mathematics with its motivating physical phenomena and, conversely, by showing how the mathematical models predict new physical phenomena.

### Mathematical Methods in Physics

This book is a text on partial differential equations (PDEs) of mathematical physics and boundary value problems, trigonometric Fourier series, and special functions. This is the core content of many courses in the fields of engineering, physics, mathematics, and applied mathematics. The accompanying software provides a laboratory environment that allows the user to generate and model different physical situations and learn by experimentation. From this standpoint, the book along with the software can also be used as a reference book on PDEs, Fourier series and special functions for students and professionals alike.

### Special Functions

Contains the various principal special functions in common use and their basic properties and manipulations. Discusses expansions of functions in infinite series and infinite product and the asymptotic expansion of functions. For physicists, engineers, and mathematicians. Acidic paper. Paper edition (unseen), $38. Annotation copyrighted by Book News, Inc., Portland, OR

### Mathematical Methods for Physicists

This new and completely revised Fourth Edition provides thorough coverage of the important mathematics needed for upper-division and graduate study in physics and engineering. Following more than 28 years of successful class-testing, Mathematical Methods for Physicists is considered the standard text on the subject. A new chapter on nonlinear methods and chaos is included, as are revisions of the differential equations and complex variables chapters. The entire book has been made even more accessible, with special attention given to clarity, completeness, and physical motivation. It is an excellent reference apart from its course use. This revised Fourth Edition includes: Modernized terminology Group theoretic methods brought together and expanded in a new chapter An entirely new chapter on nonlinear mathematical physics Significant revisions of the differential equations and complex variables chapters Many new or improved exercises Forty new or improved figures An update of computational techniques for today's contemporary tools, such as microcomputers, Numerical Recipes, and Mathematica(r), among others

### The Functions of Mathematical Physics

Comprehensive text provides a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation.

### Handbook of Mathematical Functions

An extensive summary of mathematical functions that occur in physical and engineering problems

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Author: Ian Naismith Sneddon

Publisher: N.A

ISBN: N.A

Category: Functions

Page: 184

View: 2419

*An Introduction to the Classical Functions of Mathematical Physics*

Author: Nico M. Temme

Publisher: John Wiley & Sons

ISBN: 9780471113133

Category: Mathematics

Page: 374

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*A Unified Introduction with Applications*

Author: NIKIFOROV,UVAROV

Publisher: Springer Science & Business Media

ISBN: 1475715951

Category: Mathematics

Page: 427

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Author: George Turrell

Publisher: Elsevier

ISBN: 0080511279

Category: Mathematics

Page: 424

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Author: W. W. Bell

Publisher: Courier Corporation

ISBN: 0486317560

Category: Technology & Engineering

Page: 272

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Author: Bullett Shaun,Fearn Tom,Smith Frank

Publisher: World Scientific

ISBN: 1786341018

Category: Mathematics

Page: 248

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Author: A. Chakrabarty

Publisher: New Age International

ISBN: 9788122408805

Category:

Page: 168

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*Stochastic, Circulant, and Bell Matrices*

Author: Ruben Aldrovandi

Publisher: World Scientific

ISBN: 9789812799838

Category: Mathematics

Page: 340

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*With Problems and Solutions*

Author: Michela Petrini,Gianfranco Pradisi,Alberto Zaffaroni

Publisher: World Scientific Publishing Company

ISBN: 1786343460

Category: Science

Page: 340

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Author: N. N. Lebedev

Publisher: Courier Corporation

ISBN: 0486139891

Category: Mathematics

Page: 308

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Author: Refaat El Attar

Publisher: Lulu.com

ISBN: 1411666909

Category: Mathematics

Page: 310

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Author: N.A

Publisher: Lulu.com

ISBN: 0557037638

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Author: Paula Tretkoff

Publisher: Advanced Textbooks in Mathemat

ISBN: 9781786342942

Category: Mathematics

Page: 250

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*An Introduction to Symmetry Principles, Group Representations, and Special Functions in Classical and Quantum Physics*

Author: Wu-Ki Tung

Publisher: World Scientific Publishing Company

ISBN: 981310404X

Category: Representations of groups

Page: 336

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Author: Edward K Blum,Sergey V Lototsky

Publisher: World Scientific Publishing Company

ISBN: 981310662X

Category: Science

Page: 116

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*Partial Differential Equations, Fourier Series, and Special Functions*

Author: Victor Henner,Tatyana Belozerova,Kyle Forinash

Publisher: CRC Press

ISBN: 156881335X

Category: Science

Page: 859

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Author: Z. X. Wang,D. R. Guo

Publisher: World Scientific

ISBN: 9789971506674

Category: Mathematics

Page: 695

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Author: George B. Arfken,Hans J. Weber

Publisher: Academic Press

ISBN: 1483288064

Category: Science

Page: 1029

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Author: Harry Hochstadt

Publisher: Courier Corporation

ISBN: 0486168786

Category: Science

Page: 352

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*With Formulas, Graphs, and Mathematical Tables*

Author: Milton Abramowitz,Irene A. Stegun

Publisher: Courier Corporation

ISBN: 9780486612720

Category: Mathematics

Page: 1046

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