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020 a| 9783034804301 (alk. paper);

020 a| 303480430X (alk. paper);

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049 a| EREEa| NEHH;

050 00 a| QA303.2b| .E76 2012;

100 1 a| Ernst, Thomas,d| 1960-?| UNAUTHORIZED;

245 12 a| A comprehensive treatment of q-calculush| [electronic resource] /c| Thomas Ernst.;

260 a| Basel ;a| New York :b| Birkhäuser/Springer,;

300 a| xvi, 491 p. :b| ill. ;c| 24 cm.;

504 a| Includes bibliographical references (p. 447-465) and indexes.;

505 0 a| Introduction -- The different languages of q-calculus -- Pre q-calculus -- The q-umbral calculus and semigroups - the Nørlund calculus of finite differences -- q-Stirling numbers -- The first q-functions -- q-hypergeometric series -- Sundry topics -- q-orthogonal polynomials -- q-functions of several variables -- Linear partial q-difference equations -- q-Calculus and physics.;

506 a| Available only to authorized users.;

520 3 a| To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms. For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Beyond a thorough review of the historical development of q-calculus, it also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few --c| P. [4] of cover.;

538 a| Mode of access: World Wide Web;

650 0 a| Calculus.=| ^A16009;

650 0 a| Functions, Special.=| ^A25092;

650 0 a| Hypergeometric functions.=| ^A377048;

650 7 a| Calculus.2| fast;

650 7 a| Functions, Special.2| fast;

650 7 a| Hypergeometric functions.2| fast;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2012 English Internationalu| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Flink.springer.com%2F10.1007%2F978-3-0348-0431-8;

856 40 z| Full text available from Springer Booksu| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Flink.springer.com%2F10.1007%2F978-3-0348-0431-8;

947 a| (OCoLC)ocn785072979;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 4023399-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/1/2016x| EBOOKz| JERESOURCE;

A comprehensive treatment of q-calculus / Thomas Ernst.

Author/creator	Ernst, Thomas, 1960-
Format	Electronic
Publication Info	Basel ; New York : Birkhäuser/Springer,
Description	xvi, 491 p. : ill. ; 24 cm.
Supplemental Content	Full text available from Springer Nature - Springer Mathematics and Statistics eBooks 2012 English International
Supplemental Content	Full text available from Springer Books
Subjects	Calculus. Functions, Special. Hypergeometric functions.

Contents	Introduction -- The different languages of q-calculus -- Pre q-calculus -- The q-umbral calculus and semigroups - the Nørlund calculus of finite differences -- q-Stirling numbers -- The first q-functions -- q-hypergeometric series -- Sundry topics -- q-orthogonal polynomials -- q-functions of several variables -- Linear partial q-difference equations -- q-Calculus and physics.
Summary	To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms. For instance, q-hypergeometric functions are now visually clear and easy to trace back to their hypergeometric parents. With this new notation it is also easy to see the connection between q-hypergeometric functions and the q-gamma function, something that until now has been overlooked. The book covers many topics on q-calculus, including special functions, combinatorics, and q-difference equations. Beyond a thorough review of the historical development of q-calculus, it also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few -- P. [4] of cover.
Bibliography note	Includes bibliographical references (p. 447-465) and indexes.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2012947523
ISBN	9783034804301 (alk. paper)
ISBN	303480430X (alk. paper)

A comprehensive treatment of q-calculus / Thomas Ernst.

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