Overview
Covers many topics on q-calculus, i.e. special functions, combinatorics, q-difference equations and q-Bernoulli numbers
Detailed coverage of the historical development of q-calculus
Summarizes the domains of moderns physics for which q-calculus is applicable, i.e. particle physics and supersymmetry
Introduction of a new logarithmic notation for q-calculus that supersedes the older Gaspar-Rahman notation
Includes supplementary material: sn.pub/extras
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About this book
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. Apart from a thorough review of the historical development of q-calculus, this book also presents the domains of modern physics for which q-calculus is applicable, such as particle physics and supersymmetry, to name just a few.​ Â
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: A Comprehensive Treatment of q-Calculus
Authors: Thomas Ernst
DOI: https://doi.org/10.1007/978-3-0348-0431-8
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2012
Hardcover ISBN: 978-3-0348-0430-1Published: 08 September 2012
Softcover ISBN: 978-3-0348-0806-4Published: 15 October 2014
eBook ISBN: 978-3-0348-0431-8Published: 13 September 2012
Edition Number: 1
Number of Pages: XVI, 492
Topics: Special Functions, Number Theory