Last edited by Grogor
Saturday, July 18, 2020 | History

9 edition of Basic hypergeometric series found in the catalog.

Basic hypergeometric series

by George Gasper

Written in English

Subjects:
• Hypergeometric series.

• Edition Notes

Includes bibliographical references and indexes.

Classifications The Physical Object Statement George Gasper, Mizan Rahman. Series Encyclopedia of mathematics and its applications ;, v. 96 Contributions Rahman, Mizan. LC Classifications QA353.H9 G37 2004 Pagination xxvi, 428 p. ; Number of Pages 428 Open Library OL3303891M ISBN 10 0521833574 LC Control Number 2004045686

The book provides a comprehensive introduction to the many aspects of the subject of basic hypergeometric series. The book essentially assumes no prior knowledge but eventually provides a comprehensive introduction to many important topics. After developing a . The main purpose of the book is to present a brief introduction to basic hypergeometric series and applications to partition enumeration and num-ber theory. As a short account to the theory of partitions, the ﬁrst part (Chapters A-B-C) covers the algebraic aspects (basic structures: partially.

Parameter Augmentation for Basic Hypergeometric Series, I. Mathematical Essays in honor of Gian-Carlo Rota, () Parameter Augmentation for Basic Hypergeometric Series, II. Journal of Combinatorial Theory, Series A , Cited by: basic hypergeometric series as a separate branch of mathematics) until some papers of Andrews [3, 4, 5] and later of Andrews and Askey [6, 7] began to appear in the s and early eighties. All of a sudden basic hypergeometric series became a fashionable thing to do—the "^-disease" began to spread. We.

Home» MAA Publications» MAA Reviews» Basic Hypergeometric Series and Applications. Basic Hypergeometric Series and Applications. Nathan J. Fine. The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries. MAA Review;. Buy the book Written in a wonderful expository style, this books succeeds in making its difficult subject matter accessible to a wide variety of people. Of course, mathematicians studying hypergeometric series will have great use for this book. However, non-mathematicians can also greatly benefit from reading it.

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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.4/5(1). This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained and comprehensive account of the rapidly growing field of basic hypergeometric series, or q-series.

Simplicity, clarity, deductive proofs, thoughtfully designed exercises, and useful appendices are among its by: Get this from a library. Basic hypergeometric series.

[George Gasper; Mizan Rahman] -- This updated edition will continue to meet the needs for an authoritative comprehensive analysis of the rapidly growing field of basic hypergeometric series, or q-series. It includes deductive. In addition to these exercises, notes at the end of Basic hypergeometric series book chapter point the reader to related topics.

This alone makes the book an invaluable reference to those who are interested in basic series.’ Waleed A. Al-Salam Source: Math. Reviews ‘Thus the present book, devoted to ‘q’-hypergeometric series, appears at a very timely by: The theory of partitions, founded by Euler, has led in a natural way to series involving factors of the form (l-aq)(l-aq2)(l-aqn).

These "basic hypergeometric series" or "Eulerian series" were studied system­ atically first by Heine [27]. Many early results go back to Euler, Gauss, and Jacobi. BASIC HYPERGEOMETRIC SERIES Download Basic Hypergeometric Series ebook PDF or Read Online books in PDF, EPUB, and Mobi Format.

Click Download or Read Online button to get basic hypergeometric series and applications book now. This site is like a library, Use search box in the widget to get ebook that you want. 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. This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained, and comprehensive account of the rapidly growing field of basic hypergeometric series, or q-series.

Simplicity, clarity, deductive proofs, thoughtfully designed exercises, and useful appendices are among its strengths. The first five chapters cover basic hypergeometric. Let me attempt a brief description of the subject first.

The word "Basic", though standard, is apt to cause confusion. A hypergeometric series is a power series where, if the coefficient of x n is c(n), then c(n+1)/c(n) is a rational function of n.

This implies that c(n) is a quotient of products of shifted factorials, which are themselves. The first five chapters cover basic hypergeometric series and integrals, whilst the next five are devoted to applications in various areas including Askey-Wilson integrals and orthogonal polynomials, partitions in number theory, multiple series, orthogonal polynomials in several variables, and generating functions.

Volume 96 Basic Hypergeometric Series Second Edition This revised and expanded new edition will continue to meet the need for an author-itative, up-to-date, self contained, and comprehensive account of the rapidly growing ﬁeld of basic hypergeometric series, or q File Size: KB.

This updated edition will continue to meet the needs for an authoritative comprehensive analysis of the rapidly growing field of basic hypergeometric series, or q-series. It includes deductive proofs, exercises, and useful appendices. Three new chapters have been added to this edition covering Price: $For miscellaneous summation formulas of basic hypergeometric series, the readers can consult Gasper and Rahman. This paper is organized as follows. In Section 2, we will firstly prove Theorem from a terminating summation formula in, and then, Theorem will be deduced from Theorem Cited by: 4. 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. Basic hypergeometric series have been introduced a long time ago, and important contributions go back to Euler, Heine, Rogers, Ramanujan, etc. The importance and the history of the basic hyper-geometric series is clearly indicated in Askey’s foreword to the book on basic hypergeometric series Date: Final version, Aug A solid reference on the subject. Material on generalized hypergeometric functions (starting with Gauss' hypergeometric function) is presented followed by the q analogy's. The material is advanced and is well written with a tight and readable typeface. The introduction to q series will satisfy the beginner. Mizan Rahman (Septem – January 5, ) was a Bangladeshi Canadian mathematician and writer. He specialized in fields of mathematics such as hypergeometric series and orthogonal also had interests encompassing literature, Alma mater: University of Dhaka, University of. 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. This paper is motivated by the umbral calculus approach to basic hypergeometric series as initiated by Goldman-Rota, Andrews, and Roman, et al. We develop a method of deriving hypergeometric identities by parameter augmentation, which means that a hypergeometric identity with multiple parameters may be derived from its special case obtained by Cited by:. By convention, a series P u n is called a hypergeometric series if g(n) = u n+1/u n is a rational function of n. It is called a q- (or basic) hypergeometric series if g(n) is a rational function of qn. More generally, such a series is called an elliptic hypergeometric series if g(n) is File Size: KB.This book contains a unique collection of both research and survey papers written by an international group of some of the world's experts on partitions, q-series, and modular forms, as outgrowths of a conference held at the University of Florida, Gainesville in March In the literature of basic hypergeometric series, Bailey's$_6\psi_6\$ series identity is very important.

So finding the nontrivial extension of it is a quite significative work.