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A Comprehensive Treatment of q-Calculus

Springer Basel,
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Addressing the persistently divergent views on notation that have hampered the development of q-calculus theory, this potent new notation method is based on logarithms. The book covers a multitude of q-notation topics and outlines its uses in modern physics.


Titel: A Comprehensive Treatment of q-Calculus
Autoren/Herausgeber: Thomas Ernst
Ausgabe: 2012

ISBN/EAN: 9783034804301

Seitenzahl: 492
Format: 23,5 x 15,5 cm
Produktform: Hardcover/Gebunden
Gewicht: 919 g
Sprache: Englisch

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. - Newsletter
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