A Comprehensive Treatment of q-Calculus

  • Thomas Ernst

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Thomas Ernst
    Pages 1-25
  3. Thomas Ernst
    Pages 27-61
  4. Thomas Ernst
    Pages 63-95
  5. Thomas Ernst
    Pages 169-193
  6. Thomas Ernst
    Pages 195-240
  7. Thomas Ernst
    Pages 241-277
  8. Thomas Ernst
    Pages 279-307
  9. Thomas Ernst
    Pages 309-358
  10. Thomas Ernst
    Pages 359-426
  11. Thomas Ernst
    Pages 427-440
  12. Thomas Ernst
    Pages 441-446
  13. Back Matter
    Pages 447-491

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. 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.


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

Authors and affiliations

  • Thomas Ernst
    • 1
  1. 1.Uppsala UniversityUppsalaSweden

Bibliographic information