## The Special Functions and Their Approximations

**Author**: Yudell L. Luke

**Publisher:**Academic Press

**ISBN:**0080955606

**Category:**Mathematics

**Page:**348

**View:**314

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A detailed and self-contained and unified treatment of many mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. many common features of the Bessel functions, Legendre functions, incomplete gamma functions, confluent hypergeometric functions, as well as of otherw, can be derived. Hitherto, many of the material upon which the volumes are based has been available only in papers scattered throughout the literature.

## The Special Functions and Their Approximations

**Author**: Luke,Yudell L. Luke

**Publisher:**N.A

**ISBN:**N.A

**Category:**Mathematics

**Page:**349

**View:**9483

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## CRC Concise Encyclopedia of Mathematics, Second Edition

**Author**: Eric W. Weisstein

**Publisher:**CRC Press

**ISBN:**1420035223

**Category:**Mathematics

**Page:**3252

**View:**2193

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Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopedia to include 1000 additional pages of illustrated entries. The accessibility of the Encyclopedia along with its broad coverage and economical price make it attractive to the widest possible range of readers and certainly a must for libraries, from the secondary to the professional and research levels. For mathematical definitions, formulas, figures, tabulations, and references, this is simply the most impressive compendium available.

## Handbuch für die q-Analysis

**Author**: Thomas Ernst

**Publisher:**Logos Verlag Berlin GmbH

**ISBN:**3832530991

**Category:**

**Page:**493

**View:**373

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Bis jetzt befand sich die theoretische Entwicklung der q-Analysis auf einer ungleichmäßigen Grundlage. Die sperrige Notation von Gasper-Rahman wurde in der Regel verwendet, aber die veröffentlichten Werke in der q-Analysis hatten je nach den verschiedenen Ländern und verschiedenen Mathematikern unterschiedliche Ausgangspunkte. Die Verwirrung der Sprachen hat nicht nur die theoretische Entwicklung kompliziert, sondern hat auch dazu beigetragen, dass die q-Analysis ein vernachlässigter mathematischer Bereich geworden ist. Dieses Buch überwindet diese Probleme durch die Einführung einer neuen logarithmischen Notation für die q-Analysis. Zum Beispiel sind q-hypergeometrische Funktionen nun optisch ansprechend und der Übergang zurück auf ihre hypergeometrische Vorfahren ist einfach. Mit dieser neuen Notation ist es auch leicht, den Zusammenhang zwischen den q-hypergeometrischen Funktionen und der q-Gamma-Funktion einzusehen, etwas, das früher völlig vernachlässigt wurde. Das Buch deckt viele Themen in Bezug auf die q-Analysis, zum Beispiel: spezielle Funktionen, Bernoullische Zahlen, q-Differenzengleichungen. Neben einer gründlichen Überprüfung der historischen Entwicklung der q-Analysis, zeigt dieses Buch auch die Domänen der modernen Physik, in denen die q-Analysis anwendbar ist, zum Beispiel: Teilchenphysik und Supersymmetrie, um nur einige zu nennen.

## Essential Mathematical Methods for Physicists

**Author**: Hans-Jurgen Weber,George Brown Arfken

**Publisher:**Academic Press

**ISBN:**0120598779

**Category:**Mathematics

**Page:**932

**View:**6837

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This adaptation of Arfken and Weber's bestselling 'Mathematical Methods for Physicists' is a comprehensive, accessible reference for using mathematics to solve physics problems. Introductions and review material provide context and extra support for key ideas, with detailed examples.

## Mathematics of Computation, 1943-1993

*A Half-century of Computational Mathematics : Mathematics of Computation 50th Anniversary Symposium, August 9-13, 1993, Vancouver, British Columbia*

**Author**: Walter Gautschi

**Publisher:**American Mathematical Soc.

**ISBN:**0821802917

**Category:**Mathematics

**Page:**643

**View:**1087

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This volume, containing the proceedings of an international conference commemorating the fiftieth anniversary of Mathematics of Computation, reflects the unique way in which this journal views computational mathematics as including not only numerical analysis but also computational number theory. Accordingly, the book has two parts, one for each of these two branches. The major purpose of the conference was to take stock of the current state of the field, to reflect on its recent history, and to assess future trends. This is done in substantial survey papers written by recognized experts; there are ten such surveys in the first part and four in the second. The former cover such topics as multigrid and multiresolution methods, numerical linear algebra, methods for solving differential equations, splines and their applications, optimization, and approximation methods and software for special functions. The survey papers in the second part deal with the precomputer history of integer factorization and primality testing, as well as with some of the modern techniques of factorization and with computational techniques in analytic number theory and deterministic algorithms and their complexity in algebraic number theory. A glimpse into the very active contemporary scene is provided by the forty-six short contributed papers. With extensive bibliographic references, a detailed index, and language accessible to a wide audience, this book is an authoritative resource in the field of computational mathematics.

## Mathematical Functions and Their Approximations

**Author**: Yudell L. Luke

**Publisher:**Academic Press

**ISBN:**1483262456

**Category:**Mathematics

**Page:**586

**View:**8365

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Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind. Numerical coefficients for Chebyshev expansions of the more common functions are tabulated. Other chapters contain polynomial and rational approximations for certain class of G-functions, the coefficients in the early polynomials of these rational approximations, and the Padé approximations for many of the elementary functions and the incomplete gamma functions. The remaining chapters describe the development of analytic approximations and expansions. This book will prove useful to mathematicians, advance mathematics students, and researchers.

## Walter Gautschi, Volume 1

*Selected Works with Commentaries*

**Author**: Claude Brezinski,Ahmed Sameh

**Publisher:**Springer Science & Business Media

**ISBN:**146147034X

**Category:**Mathematics

**Page:**694

**View:**5683

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Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi

## Mathematics of computation

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Education

**Page:**N.A

**View:**9536

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## Transform methods & special functions

**Author**: Peter Rusev,Ivan Dimovski,Virginia Kiryakova

**Publisher:**N.A

**ISBN:**9789548986052

**Category:**

**Page:**613

**View:**2066

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## The Publishers' Trade List Annual

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**American literature

**Page:**N.A

**View:**6131

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## International Aerospace Abstracts

**Author**: Cambridge Scientific Abstracts, Inc. Internet Database Service

**Publisher:**N.A

**ISBN:**N.A

**Category:**Aeronautics

**Page:**N.A

**View:**9718

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## Numerical Methods for Special Functions

**Author**: Amparo Gil,Javier Segura,Nico M. Temme

**Publisher:**SIAM

**ISBN:**9780898717822

**Category:**Approximation theory

**Page:**415

**View:**910

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Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. This book provides an up-to-date overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. Not only are standard and simple parameter domains considered, but methods valid for large and complex parameters are described as well. The first part of the book (basic methods) covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations. Its focus is on the computation of special functions; however, it is suitable for general numerical courses. Pseudoalgorithms are given to help students write their own algorithms. In addition to these basic tools, the authors discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions, Padé approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).

## Mathematical Analysis, Approximation Theory and Their Applications

**Author**: Themistocles M. Rassias,Vijay Gupta

**Publisher:**Springer

**ISBN:**3319312812

**Category:**Mathematics

**Page:**741

**View:**3966

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Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

## Numerical Solution of Ordinary Differential Equations

**Author**: Kendall Atkinson,Weimin Han,David E. Stewart

**Publisher:**John Wiley & Sons

**ISBN:**1118164520

**Category:**Mathematics

**Page:**272

**View:**4081

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A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

## Beginning Partial Differential Equations

**Author**: Peter V. O'Neil

**Publisher:**John Wiley & Sons

**ISBN:**1118030605

**Category:**Mathematics

**Page:**496

**View:**3056

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## Analytic Number Theory, Approximation Theory, and Special Functions

*In Honor of Hari M. Srivastava*

**Author**: Gradimir V. Milovanović,Michael Th. Rassias

**Publisher:**Springer

**ISBN:**149390258X

**Category:**Mathematics

**Page:**880

**View:**1797

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This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

## Mathematics of Classical and Quantum Physics

**Author**: Frederick W. Byron,Robert W. Fuller

**Publisher:**Courier Corporation

**ISBN:**9780486671642

**Category:**Science

**Page:**661

**View:**5934

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Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.