Comprehensive treatment of q-calculus / Thomas Ernst.

Includes bibliographical references and index.

1. Introduction --
2. The different languages of q-calculus --
3. Pre q-calculus --
4. The q-umbral calculus and semigroups. The Nørlund calculus of finite differences --
5. q-Stirling numbers --
6. The first q-functions --
7. q-hypergeometric series --
8. Sundry topics --
9. q-orthogonal polynomials --
10. q-functions of several variables --
11. Linear partial q-difference equations --
12. q-Calculus and physics.
References--
Index--

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 -- P. [4] of cover.