Hypergeometric Functions And Their Applications

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Hypergeometric Functions And Their Applications

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Author : James B. Seaborn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09

Hypergeometric Functions And Their Applications written by James B. Seaborn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Science categories.

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. ).

Multiple Hypergeometric Functions And Applications

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Author : Harold Exton
language : en
Publisher: Ellis Horwood
Release Date : 1976

Multiple Hypergeometric Functions And Applications written by Harold Exton and has been published by Ellis Horwood this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.

Generalized Associated Legendre Functions And Their Applications

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Author : Nina Opanasivna Virchenko
language : en
Publisher: World Scientific
Release Date : 2001

Generalized Associated Legendre Functions And Their Applications written by Nina Opanasivna Virchenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

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, P m, n ? ( z ) and Q m, 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 P m, n ? ( z ) and Q m, n ? ( z ), the classes of dual and triple integral equations associated with the function P m, n -1/2+i? (cha) etc. Contents: A General Information on Legendre Functions; The Generalized Associated Legendre Functions; The Series Representations of the Generalized Associated Legendre Functions; Relations Between Different Solutions of the Generalized Legendre Equation. Wronskians of Linearly Independent Solutions; Relations Between Contiguous Generalized Associated Legendre Functions; Differential Operators Generated by the Generalized Associated Legendre Equation; Asymptotic Formulas for the Generalized Associated Legendre Functions in a Neighborhood of Singular Points; Asymptotic Representations of the Generalized Associated Legendre Functions as the Functions of Parameters; Integral Representations of the Generalized Associated Legendre Functions of the First Kind; Integral Representations of the Generalized Associated Legendre Functions of the Second Kind; Zeros of the Generalized Associated Legendre Functions; Connection of the Generalized Associated Legendre Functions with the Jacobi Functions; and other topics. Readership: Graduate students and researchers in mathematics, physics and engineer

The Confluent Hypergeometric Function

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Author : Herbert Buchholz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22

The Confluent Hypergeometric Function written by Herbert Buchholz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Science categories.

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.

Q Hypergeometric Functions And Applications

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Author : Harold Exton
language : en
Publisher:
Release Date : 1983

Q Hypergeometric Functions And Applications written by Harold Exton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

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.

Classical Elliptic Hypergeometric Functions And Their Applications

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Author : V. P. Spiridonov
language : en
Publisher:
Release Date : 2005

Classical Elliptic Hypergeometric Functions And Their Applications written by V. P. Spiridonov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

Generalized Hypergeometric Functions With Applications In Statistics And Physical Sciences

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Author : A. M. Mathai
language : en
Publisher: Springer
Release Date : 2006-11-15

Generalized Hypergeometric Functions With Applications In Statistics And Physical Sciences written by A. M. Mathai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Generalized Hypergeometric Functions

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Author : K. Srinivasa Rao
language : en
Publisher:
Release Date : 2018

Generalized Hypergeometric Functions written by K. Srinivasa Rao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Hypergeometric functions categories.

"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.

Basic Hypergeometric Series And Applications

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Author : Nathan Jacob Fine
language : en
Publisher: American Mathematical Soc.
Release Date : 1988

Basic Hypergeometric Series And Applications written by Nathan Jacob Fine and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

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.

Special Issue On Generalized Hypergeometric Functions And Their Applications

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Author : Hari M. Srivastava
language : en
Publisher:
Release Date : 1996

Special Issue On Generalized Hypergeometric Functions And Their Applications written by Hari M. Srivastava and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.