Download or read book Vorlesungen ber die hypergeometrische Funktion written by Felix Klein and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bei der Herausgabe der KLEINschen Vorlesung über die hyper geometrische Funktion erschienen nur zwei Wege gangbar: Entweder eine durchgreifende Umarbeitung, auch im großen, oder eine möglichst weitgehende Erhaltung der ursprünglichen Form. Vor allem auch aus historischen Gründen wurde der letztere Weg beschritten. Daher ist die Anordnung des Stoffes erhalten geblieben; e, s ist nur, von kleinen Änderungen abgesehen, ein Exkurs über homogene Schreibweise aus der KLEINschen Vorlesung über lineare Differentialgleichungen ein gefügt, ferner sind die Schlußbemerkungen zur geometrischen Theorie im Falle komplexer Exponenten als durch die Arbeiten von F. SCHILLING überholt, weggelassen. Aus dem obengenannten Grunde sind beispiels weise auch Entwicklungen beibehalten worden, die heute schon dem Anfänger geläufig sind (etwa die Ausführungen über stereographische Projektion). In Rücksicht auf möglichste Erhaltung der KLEINschen Darstellung sind ferner Hinweise des Herausgebers auf inzwischen ge machte Fortschritte der Wissenschaft vom Texte getrennt als Anmerkun gen am Schluß zusammengestellt. Diese Hinweise erheben aber in keiner Weise den Anspruch auf Vollständigkeit. Bei der nicht zu um gehenden Revision des Textes im einzelnen ist, dem oben angegebenen Gesichtspunkt entsprechend, möglichste Wahrung des persönlichen KLEINschen Stils angestrebt. übrigens habe ich darauf Bedacht genommen, auch dem A nlänger die Lektüre durch Anmerkungen und durch Nachweise der KLEINschen Zitate zu erleichtern. Denn zweifellos bieten gerade diese Vorlesungen eine treffliche Ergänzung und Weiterführung dessen, was der Studierende mittleren Semesters an Geometrie und Funktionentheorie kennen gelernt hat.

Download or read book The International Commission on Mathematical Instruction 1908 2008 People Events and Challenges in Mathematics Education written by Fulvia Furinghetti and published by Springer Nature. This book was released on 2023-01-30 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the history of ICMI trough a prosopographical approach. In other words, it pays a lot of attention to the actors of the International movement. The portraits of the members of the ICMI Central Committees (1908-1936) and ICMI Executive Committees (1952-2008), and other eminent figures in ICMI history, who have passed away in the first 100 years of its life, are the guiding thread of the volume. Each portrait includes: · Biographical information · An outline of the various contributions made by the individual in question to the study of problems pertaining to mathematics teaching/education · Primary bibliography · Secondary with particular attention to the publications concerning the teaching of mathematics · Images: photos, book frontispieces, relevant manuscripts The authors of the portraits (30 altogether) are researchers in the history of mathematics, mathematics, and mathematics education. The focus on the officer’s role within ICMI and on his/her contributions to mathematics education, make the portraits different from usual biographies. In particular, since most officers were active mathematicians, the portraits shed light on aspects of their lesser-known activity. Connecting chapters place the action of these figures in the historical context and in the different phases of ICMI history.

Download or read book Table of Integrals Series and Products written by Daniel Zwillinger and published by Elsevier. This book was released on 2014-09-18 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The eighth edition of the classic Gradshteyn and Ryzhik is an updated completely revised edition of what is acknowledged universally by mathematical and applied science users as the key reference work concerning the integrals and special functions. The book is valued by users of previous editions of the work both for its comprehensive coverage of integrals and special functions, and also for its accuracy and valuable updates. Since the first edition, published in 1965, the mathematical content of this book has significantly increased due to the addition of new material, though the size of the book has remained almost unchanged. The new 8th edition contains entirely new results and amendments to the auxiliary conditions that accompany integrals and wherever possible most entries contain valuable references to their source. - Over 10, 000 mathematical entries - Most up to date listing of integrals, series and products (special functions) - Provides accuracy and efficiency in industry work - 25% of new material not including changes to the restrictions on results that revise the range of validity of results, which lend to approximately 35% of new updates

Download or read book Linear Differential Equations and Group Theory from Riemann to Poincare written by Jeremy Gray and published by Springer Science & Business Media. This book was released on 2010-01-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.

Download or read book Hessian Polyhedra Invariant Theory And Appell Hypergeometric Functions written by Lei Yang and published by World Scientific. This book was released on 2018-03-13 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our book gives the complex counterpart of Klein's classic book on the icosahedron. We show that the following four apparently disjoint theories: the symmetries of the Hessian polyhedra (geometry), the resolution of some system of algebraic equations (algebra), the system of partial differential equations of Appell hypergeometric functions (analysis) and the modular equation of Picard modular functions (arithmetic) are in fact dominated by the structure of a single object, the Hessian group $mathfrak{G}’_{216}$. It provides another beautiful example on the fundamental unity of mathematics.

Download or read book Table of Integrals Series and Products written by I. S. Gradshteyn and published by Academic Press. This book was released on 2014-05-10 with total page 1207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

Download or read book Special Functions and the Theory of Group Representations written by Naum I͡Akovlevich Vilenkin and published by American Mathematical Soc.. This book was released on 1978 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Complex Analysis written by Reiner Kuhnau and published by Elsevier. This book was released on 2004-12-09 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).

Download or read book Course In Analysis A Vol Iv Fourier Analysis Ordinary Differential Equations Calculus Of Variations written by Niels Jacob and published by World Scientific. This book was released on 2018-07-19 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures.Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard-Lindelöf and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm-Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows.Our introduction to the calculus of variations includes a discussion of the Euler-Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton-Jacobi theory. Related first order partial differential equations are treated in more detail.The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.

Download or read book Hypergeometric Functions Over Finite Fields written by Jenny Fuselier and published by American Mathematical Society. This book was released on 2022-11-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Download or read book The Confluent Hypergeometric Function written by Herbert Buchholz and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the higher transcendental function known as the confluent hypergeometric function. In the last two decades this function has taken on an ever increasing significance because of its use in the application of mathematics to physical and technical problems. There is no doubt that this trend will continue until the general theory of confluent hypergeometric functions becomes familiar to the majority of physicists in much the same way as the cylinder functions, which were previously less well known, are now used in many engineering and physical problems. This book is intended to further this development. The important practical significance of the functions which are treated hardly demands an involved discussion since they include, as special cases, a number of simpler special functions which have long been the everyday tool of the physicist. It is sufficient to mention that these include, among others, the logarithmic integral, the integral sine and cosine, the error integral, the Fresnel integral, the cylinder functions and the cylinder function in parabolic cylindrical coordinates. For anyone who puts forth the effort to study the confluent hypergeometric function in more detail there is the inestimable advantage of being able to understand the properties of other functions derivable from it. This gen eral point of view is particularly useful in connection with series ex pansions valid for values of the argument near zero or infinity and in connection with the various integral representations.

Download or read book New Advances in Transcendence Theory written by Alan Baker and published by Cambridge University Press. This book was released on 1988-10-13 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account of the proceedings of a very successful symposium of Transcendental Number Theory held in Durham in 1986. Most of the leading international specialists were present and the lectures reflected the great advances that have taken place in this area. The papers cover all the main branches of the subject, and include not only definitive research but valuable survey articles.

Download or read book Current Topics In Analytic Function Theory written by Shigeyoshi Owa and published by World Scientific. This book was released on 1992-12-31 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of research-and-survey articles by eminent and active workers around the world on the various areas of current research in the theory of analytic functions.Many of these articles emerged essentially from the proceedings of, and various deliberations at, three recent conferences in Japan and Korea: An International Seminar on Current Topics in Univalent Functions and Their Applications which was held in August 1990, in conjunction with the International Congress of Mathematicians at Kyoto, at Kinki University in Osaka; An International Seminar on Univalent Functions, Fractional Calculus, and Their Applications which was held in October 1990 at Fukuoka University; and also the Japan-Korea Symposium on Univalent Functions which was held in January 1991 at Gyeongsang National University in Chinju.

Download or read book Encyclopedia of Computer Science and Technology written by Jack Belzer and published by CRC Press. This book was released on 1979-10-01 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This comprehensive reference work provides immediate, fingertip access to state-of-the-art technology in nearly 700 self-contained articles written by over 900 international authorities. Each article in the Encyclopedia features current developments and trends in computers, software, vendors, and applications...extensive bibliographies of leading figures in the field, such as Samuel Alexander, John von Neumann, and Norbert Wiener...and in-depth analysis of future directions."

Download or read book Mathematics of the 19th Century written by A.N. Kolmogorov and published by Springer Science & Business Media. This book was released on 1998-03-24 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The editors of the present series had originally intended to publish an integrated work on the history of mathematics in the nineteenth century, passing systemati cally from one discipline to another in some natural order. Circumstances beyond their control, mainly difficulties in choosing authors, led to the abandonment of this plan by the time the second volume appeared. Instead of a unified mono graph we now present to the reader a series of books intended to encompass all the mathematics of the nineteenth century, but not in the order of the accepted classification of the component disciplines. In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication. 1 We recall that the first book contained essays on the history of mathemati 2 cal logic, algebra, number theory, and probability, while the second covered the history of geometry and analytic function theory. In the present third volume the reader will find: 1. An essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory" by S. N. Bernshtein. This highly original essay is due to the late N. I. Akhiezer (1901-1980), the author of fundamental discoveries in this area. Akhiezer's text will no doubt attract attention not only from historians of mathematics, but also from many specialists in constructive function theory.

Download or read book Special Functions written by Richard Beals and published by Cambridge University Press. This book was released on 2010-08-12 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.

Download or read book Elliptic and Modular Functions from Gauss to Dedekind to Hecke written by Ranjan Roy and published by Cambridge University Press. This book was released on 2017-04-18 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.