Mathematics

Special Functions

Author: George E. Andrews,Richard Askey,Ranjan Roy

Publisher: Cambridge University Press

ISBN: 9780521789882

Category: Mathematics

Page: 682

View: 6577

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

Handbuch für die q-Analysis

Author: Thomas Ernst

Publisher: Logos Verlag Berlin GmbH

ISBN: 3832530991

Category:

Page: 493

View: 2311

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.
Science

Mathematische Methoden der Physik

Author: Michael Karbach

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110461374

Category: Science

Page: 295

View: 4277

Sowohl im Studium als auch in der täglichen Arbeit benötigt der Physiker eine Vielzahl mathematischer Methoden, die über die Methoden aus den Grundvorlesungen der Analysis und linearen Algebra hinausgehen. Das vorliegende Buch baut auf diesen Vorlesungen auf und stellt die grundlegenden und jeweils einführenden Themen aus der Funktionentheorie, der Funktionalanalysis, der Theorie orthogonaler Polynome und Funktionen, der Fouriertheorie, der Tensorrechnung und der Distributionen dar. Bei der sehr kompakten Darstellung des Stoffes wurde darauf geachtet eine einheitliche und gebräuchliche Notation, über die verschiedenen Gebiete der Mathematik und Physik hinweg, zu verwenden. Besonders wurde auf eine anschauliche Präsentation des Stoffes Wert gelegt, was zum einen durch zahlreiche erklärende farbige Grafiken und zum anderen durch viele praxisrelevante Beispiele und Aufgaben mit Lösungen erreicht wurde. Der Text ist insbesondere für Physiker geeignet, aber darüber hinaus auch für Ingenieure im Selbststudium. Inhalt Funktionentheorie Spezielle Funktionen Grundlagen der Funktionalanalysis Orthogonale Funktionen Tensorrechnung Distributionen
Mathematics

Special Functions 2000: Current Perspective and Future Directions

current perspective and future directions : [proceedings of the NATO Advanced Study Institute on Special Functions 2000: Current Perspective and Future Directions, Tempe, Arizona, USA, 29 May-9 June 2000]

Author: Joaquin Bustoz,Mourad Ismail,Sergeĭ Konstantinovich Suslov

Publisher: Springer Science & Business Media

ISBN: 9780792371199

Category: Mathematics

Page: 520

View: 8682

The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painleve classification.
Mathematics

Kuznetsov's Trace Formula and the Hecke Eigenvalues of Maass Forms

Author: Andrew Knightly,C. Li

Publisher: American Mathematical Soc.

ISBN: 0821887440

Category: Mathematics

Page: 132

View: 3167

The authors give an adelic treatment of the Kuznetsov trace formula as a relative trace formula on $\operatorname{GL}(2)$ over $\mathbf{Q}$. The result is a variant which incorporates a Hecke eigenvalue in addition to two Fourier coefficients on the spectral side. The authors include a proof of a Weil bound for the generalized twisted Kloosterman sums which arise on the geometric side. As an application, they show that the Hecke eigenvalues of Maass forms at a fixed prime, when weighted as in the Kuznetsov formula, become equidistributed relative to the Sato-Tate measure in the limit as the level goes to infinity.
Mathematics

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: 1438

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

Boolean Functions

Theory, Algorithms, and Applications

Author: Yves Crama,Peter L. Hammer

Publisher: Cambridge University Press

ISBN: 1139498630

Category: Mathematics

Page: N.A

View: 2122

Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.
Logic, Symbolic and mathematical

Principia Mathematica.

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 9562

Science

Encyclopedia of mathematical physics

Author: Sheung Tsun Tsou

Publisher: Academic Pr

ISBN: 9780125126601

Category: Science

Page: 3500

View: 737

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originated from work in mathematical physics by providing them with focused high quality background information. * First comprehensive interdisciplinary coverage * Mathematical Physics explained to stimulate new developments and foster new applications of its methods to other fields * Written by an international group of experts * Contains several undergraduate-level introductory articles to facilitate acquisition of new expertise * Thematic index and extensive cross-referencing to provide easy access and quick search functionality * Also available online with active linking.
Mathematics

Fuchsian Differential Equations

With Special Emphasis on the Gauss-Schwarz Theory

Author: Masaaki Yoshida

Publisher: Springer-Verlag

ISBN: 3663141152

Category: Mathematics

Page: 215

View: 6828

Mathematics

Advances in Inequalities for Special Functions

Author: Pietro Cerone,Sever Silvestru Dragomir

Publisher: Nova Science Pub Incorporated

ISBN: N.A

Category: Mathematics

Page: 170

View: 9631

This book is the first in a collection of research monographs that are devoted to presenting recent research, development and use of Mathematical Inequalities for Special Functions. All the papers incorporated in the book have peen peer-reviewed and cover a range of topics that include both survey material of previously published works as well as new results. In his presentation on special functions approximations and bounds via integral representation, Pietro Cerone utilises the classical Stevensen inequality and bounds for the Ceby sev functional to obtain bounds for some classical special functions. The methodology relies on determining bounds on integrals of products of functions. The techniques are used to obtain novel and useful bounds for the Bessel function of the first kind, the Beta function, the Zeta function and Mathieu series.
Functional analysis

Report

Author: N.A

Publisher: N.A

ISBN: 9789513909116

Category: Functional analysis

Page: 18

View: 3543