A Comprehensive Treatment of q-Calculus

A Comprehensive Treatment of q-Calculus
Author :
Publisher : Springer Science & Business Media
Total Pages : 491
Release :
ISBN-10 : 9783034804301
ISBN-13 : 303480430X
Rating : 4/5 (01 Downloads)

Book Synopsis A Comprehensive Treatment of q-Calculus by : Thomas Ernst

Download or read book A Comprehensive Treatment of q-Calculus written by Thomas Ernst and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.​


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