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.