Items related to Basic Hypergeometric Series and Applications (Mathematical...

Basic Hypergeometric Series and Applications (Mathematical Surveys & Monographs) - Hardcover

 
9780821815243: Basic Hypergeometric Series and Applications (Mathematical Surveys & Monographs)

Synopsis

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.

"synopsis" may belong to another edition of this title.

Review

Rich with examples and results from the theory of partitions, the study of Ramanujan's mock theta functions, and modular equations. --Mathematical Reviews

"About this title" may belong to another edition of this title.

Buy Used

Condition: Very Good
Zustand: Gut | Sprache: Englisch...
View this item

US$ 122.44 shipping from Germany to U.S.A.

Destination, rates & speeds

Search results for Basic Hypergeometric Series and Applications (Mathematical...

Stock Image

Fine, Nathan J.
ISBN 10: 0821815245 ISBN 13: 9780821815243
Used Hardcover

Seller: Buchpark, Trebbin, Germany

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Condition: Gut. Zustand: Gut | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 41626202/203

Contact seller

Buy Used

US$ 30.17
Convert currency
Shipping: US$ 122.44
From Germany to U.S.A.
Destination, rates & speeds

Quantity: 1 available

Add to basket

Stock Image

Fine, Nathan J.
ISBN 10: 0821815245 ISBN 13: 9780821815243
Used Hardcover

Seller: Buchpark, Trebbin, Germany

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Condition: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 41626202/202

Contact seller

Buy Used

US$ 30.17
Convert currency
Shipping: US$ 122.44
From Germany to U.S.A.
Destination, rates & speeds

Quantity: 1 available

Add to basket

Stock Image

Fine, Nathan J.
Published by American Mathematical Society, 1988
ISBN 10: 0821815245 ISBN 13: 9780821815243
New Hardcover

Seller: GreatBookPrices, Columbia, MD, U.S.A.

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Condition: New. Seller Inventory # 5914479-n

Contact seller

Buy New

US$ 150.37
Convert currency
Shipping: US$ 2.64
Within U.S.A.
Destination, rates & speeds

Quantity: 2 available

Add to basket

Stock Image

Fine
Published by American Mathematical Society, 1988
ISBN 10: 0821815245 ISBN 13: 9780821815243
New Hardcover

Seller: Kennys Bookshop and Art Galleries Ltd., Galway, GY, Ireland

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Condition: New. 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. Series: Mathematical Surveys and Monographs. Num Pages: 124 pages. BIC Classification: PBK. Category: (G) General (US: Trade); (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 260 x 176 x 13. Weight in Grams: 436. . 1988. Hardcover. . . . . Seller Inventory # V9780821815243

Contact seller

Buy New

US$ 141.13
Convert currency
Shipping: US$ 12.24
From Ireland to U.S.A.
Destination, rates & speeds

Quantity: 1 available

Add to basket

Stock Image

Fine
Published by American Mathematical Society, 1988
ISBN 10: 0821815245 ISBN 13: 9780821815243
New Hardcover

Seller: Kennys Bookstore, Olney, MD, U.S.A.

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Condition: New. 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. Series: Mathematical Surveys and Monographs. Num Pages: 124 pages. BIC Classification: PBK. Category: (G) General (US: Trade); (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 260 x 176 x 13. Weight in Grams: 436. . 1988. Hardcover. . . . . Books ship from the US and Ireland. Seller Inventory # V9780821815243

Contact seller

Buy New

US$ 162.08
Convert currency
Shipping: US$ 10.50
Within U.S.A.
Destination, rates & speeds

Quantity: 1 available

Add to basket

Stock Image

Fine, Nathan J.
Published by American Mathematical Society, 1988
ISBN 10: 0821815245 ISBN 13: 9780821815243
Used Hardcover

Seller: GreatBookPrices, Columbia, MD, U.S.A.

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Condition: As New. Unread book in perfect condition. Seller Inventory # 5914479

Contact seller

Buy Used

US$ 172.67
Convert currency
Shipping: US$ 2.64
Within U.S.A.
Destination, rates & speeds

Quantity: 2 available

Add to basket

Seller Image

Nathan J. Fine
ISBN 10: 0821815245 ISBN 13: 9780821815243
New Paperback

Seller: Rarewaves.com USA, London, LONDO, United Kingdom

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Paperback. Condition: New. 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. Seller Inventory # LU-9780821815243

Contact seller

Buy New

US$ 186.92
Convert currency
Shipping: FREE
From United Kingdom to U.S.A.
Destination, rates & speeds

Quantity: 1 available

Add to basket

Stock Image

Nathan J. Fine
Published by American Mathematical Society, 1988
ISBN 10: 0821815245 ISBN 13: 9780821815243
New Paperback / softback

Seller: THE SAINT BOOKSTORE, Southport, United Kingdom

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Paperback / softback. Condition: New. New copy - Usually dispatched within 4 working days. 474. Seller Inventory # B9780821815243

Contact seller

Buy New

US$ 171.61
Convert currency
Shipping: US$ 15.44
From United Kingdom to U.S.A.
Destination, rates & speeds

Quantity: 2 available

Add to basket

Stock Image

Fine, Nathan J.
Published by American Mathematical Society, 1988
ISBN 10: 0821815245 ISBN 13: 9780821815243
New Hardcover

Seller: GreatBookPricesUK, Woodford Green, United Kingdom

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Condition: New. Seller Inventory # 5914479-n

Contact seller

Buy New

US$ 171.60
Convert currency
Shipping: US$ 20.16
From United Kingdom to U.S.A.
Destination, rates & speeds

Quantity: 2 available

Add to basket

Stock Image

Fine, Nathan J.
Published by American Mathematical Society, 1988
ISBN 10: 0821815245 ISBN 13: 9780821815243
Used Hardcover

Seller: GreatBookPricesUK, Woodford Green, United Kingdom

Seller rating 5 out of 5 stars 5-star rating, Learn more about seller ratings

Condition: As New. Unread book in perfect condition. Seller Inventory # 5914479

Contact seller

Buy Used

US$ 179.89
Convert currency
Shipping: US$ 20.16
From United Kingdom to U.S.A.
Destination, rates & speeds

Quantity: 2 available

Add to basket

There are 3 more copies of this book

View all search results for this book