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A Comprehensive Treatment of q-Calculus

Authors: Ernst, Thomas

  • 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
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eBook $109.00
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  • ISBN 978-3-0348-0431-8
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Hardcover $149.00
price for USA
  • ISBN 978-3-0348-0430-1
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  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
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  • ISBN 978-3-0348-0806-4
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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.​  

Table of contents (12 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0431-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0348-0430-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-0348-0806-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A Comprehensive Treatment of q-Calculus
Authors
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0431-8
DOI
10.1007/978-3-0348-0431-8
Hardcover ISBN
978-3-0348-0430-1
Softcover ISBN
978-3-0348-0806-4
Edition Number
1
Number of Pages
XVI, 492
Topics