## About this book

### Introduction

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.

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### Bibliographic information

- DOI https://doi.org/10.1007/978-3-0348-0431-8
- Copyright Information Springer Basel 2012
- Publisher Name Birkhäuser, Basel
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-0348-0430-1
- Online ISBN 978-3-0348-0431-8
- Buy this book on publisher's site