Basic Hypergeometric Series Applications

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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.

Basic Hypergeometric Series

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Author : George Gasper
language : en
Publisher:
Release Date : 2011-02-25

Basic Hypergeometric Series written by George Gasper and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-25 with Mathematics categories.

Significant revision of classic reference in special functions.

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.

Basic Hypergeometric Series Applications

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Author : Nathan Jacob Fine
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-06-06

Basic Hypergeometric Series Applications written by Nathan Jacob Fine and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-06 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.

Q Series With Applications To Combinatorics Number Theory And Physics

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Author : Bruce C. Berndt
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Q Series With Applications To Combinatorics Number Theory And Physics written by Bruce C. Berndt 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 2001 with Mathematics categories.

The subject of $q$-series can be said to begin with Euler and his pentagonal number theorem. In fact, $q$-series are sometimes called Eulerian series. Contributions were made by Gauss, Jacobi, and Cauchy, but the first attempt at a systematic development, especially from the point of view of studying series with the products in the summands, was made by E. Heine in 1847. In the latter part of the nineteenth and in the early part of the twentieth centuries, two Englishmathematicians, L. J. Rogers and F. H. Jackson, made fundamental contributions. In 1940, G. H. Hardy described what we now call Ramanujan's famous $ 1\psi 1$ summation theorem as ``a remarkable formula with many parameters.'' This is now one of the fundamental theorems of the subject. Despite humble beginnings,the subject of $q$-series has flourished in the past three decades, particularly with its applications to combinatorics, number theory, and physics. During the year 2000, the University of Illinois embraced The Millennial Year in Number Theory. One of the events that year was the conference $q$-Series with Applications to Combinatorics, Number Theory, and Physics. This event gathered mathematicians from the world over to lecture and discuss their research. This volume presents nineteen of thepapers presented at the conference. The excellent lectures that are included chart pathways into the future and survey the numerous applications of $q$-series to combinatorics, number theory, and physics.

Theory And Applications Of Special Functions For Scientists And Engineers

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Author : Xiao-Jun Yang
language : en
Publisher: Springer Nature
Release Date : 2022-01-14

Theory And Applications Of Special Functions For Scientists And Engineers written by Xiao-Jun Yang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-14 with Mathematics categories.

This book provides the knowledge of the newly-established supertrigonometric and superhyperbolic functions with the special functions such as Mittag-Leffler, Wiman, Prabhakar, Miller-Ross, Rabotnov, Lorenzo-Hartley, Sonine, Wright and Kohlrausch-Williams-Watts functions, Gauss hypergeometric series and Clausen hypergeometric series. The special functions can be considered to represent a great many of the real-world phenomena in mathematical physics, engineering and other applied sciences. The audience benefits of new and original information and references in the areas of the special functions applied to model the complex problems with the power-law behaviors. The results are important and interesting for scientists and engineers to represent the complex phenomena arising in applied sciences therefore graduate students and researchers in mathematics, physics and engineering might find this book appealing.

Theory And Applications Of Special Functions

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Author : Mourad E. H. Ismail
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Theory And Applications Of Special Functions written by Mourad E. H. Ismail 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 2006-03-30 with Mathematics categories.

This volume, "Theory and Applications of Special Functions," is d- icated to Mizan Rahman in honoring him for the many important c- tributions to the theory of special functions that he has made over the years, and still continues to make. Some of the papers were presented at a special session of the American Mathematical Society Annual Meeting in Baltimore, Maryland, in January 2003 organized by Mourad Ismail. Mizan Rahman's contributions are not only contained in his own - pers, but also indirectly in other papers for which he supplied useful and often essential information. We refer to the paper on his mathematics in this volume for more information. This paper contains some personal recollections and tries to describe Mizan Rahman's literary writings in his mother tongue, Bengali. An even more personal paper on Mizan Rahman is the letter by his sons, whom we thank for allowing us to reproduce it in this book. The theory of special functions is very much an application driven field of mathematics. This is a very old field, dating back to the 18th century when physicists and mathematician were looking for solutions of the fundamental differential equations of mathematical physics. Since then the field has grown enormously, and this book reflects only part of the known applications.

Theory And Application Of Special Functions

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Author : Richard Askey
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Theory And Application Of Special Functions written by Richard Askey and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Theory and Application of Special Functions contains the proceedings of the Advanced Seminar on Special Functions sponsored by the Mathematics Research Center of the University of Wisconsin-Madison and held from March 31 to April 2, 1975. The seminar tackled the theory and application of special functions and covered topics ranging from the asymptotic estimation of special functions to association schemes and coding theory. Some interesting results, conjectures, and problems are given. Comprised of 13 chapters, this book begins with a survey of computational methods in special functions, followed by a discussion on unsolved problems in the asymptotic estimation of special functions. The reader is then introduced to periodic Bernoulli numbers, summation formulas, and applications; problems and prospects for basic hypergeometric functions; and linear growth models with many types and multidimensional Hahn polynomials. Subsequent chapters explore two-variable analogues of the classical orthogonal polynomials; special functions of matrix and single argument in statistics; and some properties of the determinants of orthogonal polynomials. This monograph is intended primarily for students and practitioners of mathematics.

Partitions Q Series And Modular Forms

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Author : Krishnaswami Alladi
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-01

Partitions Q Series And Modular Forms written by Krishnaswami Alladi 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 2011-11-01 with Mathematics categories.

Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.

Q Series Their Development And Application In Analysis Number Theory Combinatorics Physics And Computer Algebra

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Author : George E. Andrews
language : en
Publisher: American Mathematical Soc.
Release Date : 1986

Q Series Their Development And Application In Analysis Number Theory Combinatorics Physics And Computer Algebra written by George E. Andrews 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 1986 with Mathematics categories.

Integrates developments and related applications in $q$-series with a historical development of the field. This book develops important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory.