Download or read book Expansion Problems in Connection with the Hypergeometric Differential Equation written by Bernhard Paul Reinsch and published by . This book was released on 1925 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global Analysis in Linear Differential Equations written by M. Kohno and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering. The cffcctivity of these functions is essentially due to their "behavior in the large" . For instance, the Airy function plays a basic role in the asymptotic analysis of many functions arising as solutions of differential equations in several problems of applied math ematics. In case of the employment of its behavior, one should always pay attention to the Stokes phenomenon. On the other hand, as is well-known, the Gauss hypergeometric function arises in all fields of mathematics, e.g., in number theory, in the theory of groups and in analysis itself. It is not too much to say that all power series are special or extended cases of the hypergeometric series. For the full use of its properties, one needs connection formulas or contiguous relations.
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 American Journal of Mathematics written by and published by . This book was released on 1924 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Trends And Developments In Ordinary Differential Equations Proceedings Of The International Symposium written by Philip Po-fang Hsieh and published by World Scientific. This book was released on 1994-04-08 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume which honors Professors W A Harris, Jr, M Iwano, Y Sibuya, active researchers from around the world report on their latest research results. Topics include Analytic Theory of Linear and Nonlinear Differential Equations, Asymptotic Expansions, Turning Points Theory, Special Functions, Delay Equations, Boundary Value Problems, Sturm-Liouville Eigenvalues, Periodic Solutions, Numerical Solutions and other areas of Applied Mathematics.
Download or read book Hypergeometric Functions and Their Applications written by James B. Seaborn and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface A wide range of problems exists in classical and quantum physics, engi neering, and applied mathematics in which special functions arise. The procedure followed in most texts on these topics (e. g. , quantum mechanics, electrodynamics, modern physics, classical mechanics, etc. ) is to formu late the problem as a differential equation that is related to one of several special differential equations (Hermite's, Bessel's, Laguerre's, Legendre's, etc. ).
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 Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1924 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of Hypergeometric Functions written by Kazuhiko Aomoto and published by Springer Science & Business Media. This book was released on 2011-05-21 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy a holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy a holonomic system of linear difference equations with respect to the exponents. These are deduced from Grothendieck-Deligne’s rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoff’s classical theory on analytic difference equations on the other.
Download or read book The Mathematical Gazette written by and published by . This book was released on 1926 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Formal And Analytic Solutions Of Differential Equations written by Galina Filipuk and published by World Scientific. This book was released on 2022-03-03 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides the reader with an overview of the actual state of research in ordinary and partial differential equations in the complex domain. Topics include summability and asymptotic study of both ordinary and partial differential equations, and also q-difference and differential-difference equations. This book will be of interest to researchers and students who wish to expand their knowledge of these fields.With the latest results and research developments and contributions from experts in their field, Formal and Analytic Solutions of Differential Equations provides a valuable contribution to methods, techniques, different mathematical tools, and study calculations.
Download or read book Programs of the Final Examinations for the Degree of Doctor of Philosophy written by University of Illinois (Urbana-Champaign campus). Graduate School and published by . This book was released on 1924 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences written by A. M. Mathai and published by Springer. This book was released on 2006-11-15 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The American Mathematical Monthly written by and published by . This book was released on 1925 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes section "Recent publications."
Download or read book Special Functions written by Sergeĭ I︠U︡rʹevich Slavi︠a︡nov and published by Oxford University Press, USA. This book was released on 2000 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in the complex domain. The number and characteristics of the singularities serve as a basis for classification of each individual special function. Links between linear special functions (as solutions of linear second-order equations), and non-linear special functions (as solutions of Painlevé equations) are presented as a basic and new result. Many applications to different areas of physics are shown and discussed. The book is written from a practical point of view and will address all those scientists whose work involves applications of mathematical methods. Lecturers, graduate students and researchers will find this a useful text and reference work.
Download or read book Science written by John Michels (Journalist) and published by . This book was released on 1924 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Second Course in Ordinary Differential Equations for Scientists and Engineers written by Mayer Humi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world abounds with introductory texts on ordinary differential equations and rightly so in view of the large number of students taking a course in this subject. However, for some time now there is a growing need for a junior-senior level book on the more advanced topics of differential equations. In fact the number of engineering and science students requiring a second course in these topics has been increasing. This book is an outgrowth of such courses taught by us in the last ten years at Worcester Polytechnic Institute. The book attempts to blend mathematical theory with nontrivial applications from varipus disciplines. It does not contain lengthy proofs of mathemati~al theorems as this would be inappropriate for its intended audience. Nevertheless, in each case we motivated these theorems and their practical use through examples and in some cases an "intuitive proof" is included. In view of this approach the book could be used also by aspiring mathematicians who wish to obtain an overview of the more advanced aspects of differential equations and an insight into some of its applications. We have included a wide range of topics in order to afford the instructor the flexibility in designing such a course according to the needs of the students. Therefore, this book contains more than enough material for a one semester course.
