Hypergeometric Functions And Their Applications

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Hypergeometric Functions and Their Applications

James B. Seaborn
Hypergeometric Functions and Their Applications Book PDF

Author : James B. Seaborn
Publisher : Springer Science & Business Media
Page : 261 pages
File Size : 51,7 Mb
Release : 2013-04-09
Category : Science
ISBN : 9781475754438

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Hypergeometric Functions and Their Applications by James B. Seaborn Pdf

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. ).

The Confluent Hypergeometric Function

Herbert Buchholz
The Confluent Hypergeometric Function Book PDF

Author : Herbert Buchholz
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 47,9 Mb
Release : 2013-11-22
Category : Science
ISBN : 9783642883965

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The Confluent Hypergeometric Function by Herbert Buchholz Pdf

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.

Basic Hypergeometric Series and Applications

Nathan Jacob Fine
Basic Hypergeometric Series and Applications Book PDF

Author : Nathan Jacob Fine
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 40,5 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821815243

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Basic Hypergeometric Series and Applications by Nathan Jacob Fine Pdf

The theory of partitions, founded by Euler, has led in a natural way to the idea of basic hypergeometric series, also known as Eulerian series. These series were first studied systematically by Heine, but many early results are attributed to Euler, Gauss, and Jacobi. Today, research in $q$-hypergeometric series is very active, and there are now major interactions with Lie algebras, combinatorics, special functions, and number theory. However, the theory has been developed to such an extent and with such a profusion of powerful and general results that the subject can appear quite formidable to the uninitiated. By providing a simple approach to basic hypergeometric series, this book provides an excellent elementary introduction to the subject. The starting point is a simple function of several variables satisfying a number of $q$-difference equations.The author presents an elementary method for using these equations to obtain transformations of the original function. A bilateral series, formed from this function, is summed as an infinite product, thereby providing an elegant and fruitful result which goes back to Ramanujan. By exploiting a special case, the author is able to evaluate the coefficients of several classes of infinite products in terms of divisor sums. He also touches on general transformation theory for basic series in many variables and the basic multinomial, which is a generalization of a finite sum. These developments lead naturally to the arithmetic domains of partition theory, theorems of Liouville type, and sums of squares.Contact is also made with the mock theta-functions of Ramanujan, which are linked to the rank of partitions. The author gives a number of examples of modular functions with multiplicative coefficients, along with the beginnings of an elementary constructive approach to the field of modular equations. Requiring only an undergraduate background in mathematics, this book provides a rapid entry into the field. Students of partitions, basic series, theta-functions, and modular equations, as well as research mathematicians interested in an elementary approach to these areas, will find this book useful and enlightening. Because of the simplicity of its approach and its accessibility, this work may prove useful as a textbook.

Basic Hypergeometric Series

George Gasper,Mizan Rahman
Basic Hypergeometric Series Book PDF

Author : George Gasper,Mizan Rahman
Publisher : Unknown
Page : 456 pages
File Size : 40,7 Mb
Release : 2011-02-25
Category : Mathematics
ISBN : 9780511889189

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Basic Hypergeometric Series by George Gasper,Mizan Rahman Pdf

Significant revision of classic reference in special functions.

Generalized Hypergeometric Functions

K. Srinivasa Rao,Vasudevan Lakshminarayanan
Generalized Hypergeometric Functions Book PDF

Author : K. Srinivasa Rao,Vasudevan Lakshminarayanan
Publisher : Unknown
Page : 0 pages
File Size : 55,5 Mb
Release : 2018
Category : Hypergeometric functions
ISBN : 0750314966

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Generalized Hypergeometric Functions by K. Srinivasa Rao,Vasudevan Lakshminarayanan Pdf

"In 1813, Gauss first outlined his studies of the hypergeometric series which has been of great significance in the mathematical modelling of physical phenomena. This detailed monograph outlines the fundamental relationships between the hypergeometric function and special functions. In nine comprehensive chapters, Dr. Rao and Dr. Lakshminarayanan present a unified approach to the study of special functions of mathematics using Group theory. The book offers fresh insight into various aspects of special functions and their relationship, utilizing transformations and group theory and their applications. It will lay the foundation for deeper understanding by both experienced researchers and novice students." -- Prové de l'editor.

Q-hypergeometric Functions and Applications

Harold Exton
Q hypergeometric Functions and Applications Book PDF

Author : Harold Exton
Publisher : Unknown
Page : 360 pages
File Size : 42,8 Mb
Release : 1983
Category : Mathematics
ISBN : UOM:39015015699039

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Q-hypergeometric Functions and Applications by Harold Exton Pdf

Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.

Special Functions & Their Applications

N. N. Lebedev
Special Functions Their Applications Book PDF

Author : N. N. Lebedev
Publisher : Courier Corporation
Page : 340 pages
File Size : 47,6 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486139890

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Special Functions & Their Applications by N. N. Lebedev Pdf

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.

Generalized Associated Legendre Functions And Their Applications

Iryna Fedotova,Nina Virchenko
Generalized Associated Legendre Functions And Their Applications Book PDF

Author : Iryna Fedotova,Nina Virchenko
Publisher : World Scientific
Page : 217 pages
File Size : 52,5 Mb
Release : 2001-04-30
Category : Mathematics
ISBN : 9789814492812

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Generalized Associated Legendre Functions And Their Applications by Iryna Fedotova,Nina Virchenko Pdf

The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions ρFq, Meijer's G-function, Fox's H-function, etc.Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions.This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, Pm,nκ(z) and Qm,nκ(z), which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions.The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions Pm,nκ(z) and Qm,nκ(z), the classes of dual and triple integral equations associated with the function Pm,n-1/2+iς(chα) etc.

Theory of Hypergeometric Functions

Kazuhiko Aomoto,Michitake Kita
Theory of Hypergeometric Functions Book PDF

Author : Kazuhiko Aomoto,Michitake Kita
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 40,9 Mb
Release : 2011-05-21
Category : Mathematics
ISBN : 9784431539384

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Theory of Hypergeometric Functions by Kazuhiko Aomoto,Michitake Kita Pdf

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.

Tau Functions and their Applications

John Harnad,Ferenc Balogh
Tau Functions and their Applications Book PDF

Author : John Harnad,Ferenc Balogh
Publisher : Cambridge University Press
Page : 549 pages
File Size : 47,8 Mb
Release : 2021-02-04
Category : Mathematics
ISBN : 9781108492683

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Tau Functions and their Applications by John Harnad,Ferenc Balogh Pdf

A thorough introduction to tau functions, from the basics through to the most recent results, with applications in mathematical physics.

Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications

Donald St. P. Richards
Hypergeometric Functions on Domains of Positivity Jack Polynomials and Applications Book PDF

Author : Donald St. P. Richards
Publisher : American Mathematical Soc.
Page : 259 pages
File Size : 55,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851593

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Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications by Donald St. P. Richards Pdf

This book is the first set of proceedings to be devoted entirely to the theory of hypergeometric functions defined on domains of positivity. Most of the scientific areas in which these functions are applied include analytic number theory, combinatorics, harmonic analysis, random walks, representation theory, and mathematical physics--are represented here. This volume is based largely on lectures presented at a Special Session at the AMS meeting in Tampa, Florida in March 1991, which was devoted to hypergeometric functions of matrix argument and to fostering communication among representatives of the diverse scientific areas in which these functions are utilized. Accessible to graduate students and others seeking an introduction to the state of the art in this area, this book is a suitable text for advanced graduate seminar courses for it contains many open problems.