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Birkhäuser - Birkhäuser Mathematics | A Comprehensive Treatment of q-Calculus

A Comprehensive Treatment of q-Calculus

Ernst, Thomas

2012, XVI, 492 p.

A product of Birkhäuser Basel
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  • 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

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.

Content Level » Research

Keywords » q-Appell function - q-Bernoulli numbers - q-gamma function - q-hypergeometric functions - tilde operator

Related subjects » Birkhäuser Mathematics

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