Hypergeometric Functions And Their Applications

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Hypergeometric Functions and Their Applications

Author : James B. Seaborn
Publisher : Springer Science & Business Media
ISBN 13 : 1475754434
Total Pages : 261 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Hypergeometric Functions and Their Applications by : James B. Seaborn

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. ).

Basic Hypergeometric Series and Applications

Author : Nathan Jacob Fine
Publisher : American Mathematical Soc.
ISBN 13 : 0821815245
Total Pages : 142 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Basic Hypergeometric Series and Applications by : Nathan Jacob Fine

Download or read book Basic Hypergeometric Series and Applications written by Nathan Jacob Fine and published by American Mathematical Soc.. This book was released on 1988 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This book provides a simple approach to basic hypergeometric series.

The Confluent Hypergeometric Function

Author : Herbert Buchholz
Publisher : Springer Science & Business Media
ISBN 13 : 3642883966
Total Pages : 255 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis The Confluent Hypergeometric Function by : Herbert Buchholz

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.

Basic Hypergeometric Series

Author : George Gasper
Publisher :
ISBN 13 : 0511889186
Total Pages : 456 pages
Book Rating : 4.5/5 (118 download)

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Book Synopsis Basic Hypergeometric Series by : George Gasper

Download or read book Basic Hypergeometric Series written by George Gasper and published by . This book was released on 2011-02-25 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant revision of classic reference in special functions.

Theory of Hypergeometric Functions

Author : Kazuhiko Aomoto
Publisher : Springer Science & Business Media
ISBN 13 : 4431539387
Total Pages : 327 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Theory of Hypergeometric Functions by : Kazuhiko Aomoto

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.

Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences

Author : A. M. Mathai
Publisher : Springer
ISBN 13 : 3540378006
Total Pages : 322 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences by : A. M. Mathai

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:

Special Functions & Their Applications

Author : N. N. Lebedev
Publisher : Courier Corporation
ISBN 13 : 0486139891
Total Pages : 340 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Special Functions & Their Applications by : N. N. Lebedev

Download or read book Special Functions & Their Applications written by N. N. Lebedev and published by Courier Corporation. This book was released on 2012-04-30 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Hypergeometric Functions

Author : K. Srinivasa Rao
Publisher :
ISBN 13 : 9780750314961
Total Pages : 0 pages
Book Rating : 4.3/5 (149 download)

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Book Synopsis Generalized Hypergeometric Functions by : K. Srinivasa Rao

Download or read book Generalized Hypergeometric Functions written by K. Srinivasa Rao and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Multiple Hypergeometric Functions and Applications

Author : Harold Exton
Publisher : Ellis Horwood
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Multiple Hypergeometric Functions and Applications by : Harold Exton

Download or read book Multiple Hypergeometric Functions and Applications written by Harold Exton and published by Ellis Horwood. This book was released on 1976 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Q-hypergeometric Functions and Applications

Author : Harold Exton
Publisher :
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Q-hypergeometric Functions and Applications by : Harold Exton

Download or read book Q-hypergeometric Functions and Applications written by Harold Exton and published by . This book was released on 1983 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Generalized Associated Legendre Functions and Their Applications

Author : Nina Opanasivna Virchenko
Publisher : World Scientific
ISBN 13 : 9810243537
Total Pages : 217 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Generalized Associated Legendre Functions and Their Applications by : Nina Opanasivna Virchenko

Download or read book Generalized Associated Legendre Functions and Their Applications written by Nina Opanasivna Virchenko and published by World Scientific. This book was released on 2001 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ?Fq, 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, n?(z) and Qm, n?(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, n?(z) and Qm, n?(z), the classes of dual and triple integral equations associated with the function Pm, n-1/2+i?(chà) etc.

Special Functions

Author : George E. Andrews
Publisher : Cambridge University Press
ISBN 13 : 9780521789882
Total Pages : 684 pages
Book Rating : 4.7/5 (898 download)

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Book Synopsis Special Functions by : George E. Andrews

Download or read book Special Functions written by George E. Andrews and published by Cambridge University Press. This book was released on 1999 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

Generalized Hypergeometric Functions

Author : Bernard M. Dwork
Publisher :
ISBN 13 :
Total Pages : 206 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Generalized Hypergeometric Functions by : Bernard M. Dwork

Download or read book Generalized Hypergeometric Functions written by Bernard M. Dwork and published by . This book was released on 1990 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph by one of the foremost experts on hypergeometric functions is concerned with the Boyarsky principle, developing a theory which is broad enough to encompass several of the most important hypergeometric functions.

An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions

Author : Xiao-Jun Yang
Publisher : Academic Press
ISBN 13 : 0128241543
Total Pages : 502 pages
Book Rating : 4.1/5 (282 download)

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Book Synopsis An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions by : Xiao-Jun Yang

Download or read book An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions written by Xiao-Jun Yang and published by Academic Press. This book was released on 2021-02-11 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering. Provides a historical overview for a family of the special polynomials Presents a logical investigation of a family of the hypergeometric series Proposes a new family of the hypergeometric supertrigonometric functions Presents a new family of the hypergeometric superhyperbolic functions

A = B

Author : Marko Petkovsek
Publisher : CRC Press
ISBN 13 : 1439864500
Total Pages : 231 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis A = B by : Marko Petkovsek

Download or read book A = B written by Marko Petkovsek and published by CRC Press. This book was released on 1996-01-01 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics.From the ta

Generalized Hypergeometric Functions

Author : Lucy Joan Slater
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (493 download)

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Book Synopsis Generalized Hypergeometric Functions by : Lucy Joan Slater

Download or read book Generalized Hypergeometric Functions written by Lucy Joan Slater and published by . This book was released on 1993 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The H-Function

Author : A.M. Mathai
Publisher : Springer Science & Business Media
ISBN 13 : 1441909168
Total Pages : 276 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis The H-Function by : A.M. Mathai

Download or read book The H-Function written by A.M. Mathai and published by Springer Science & Business Media. This book was released on 2009-10-10 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.