A Comprehensive Treatment of q-CalculusSpringer Science & Business Media, 13 de set. 2012 - 492 pàgines 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. |
Continguts
1 | |
The different languages of qcalculus | 27 |
Pre qAnalysis | 63 |
The qumbral calculus and semigroups The Nørlund calculus of finite differences | 97 |
qStirling numbers | 169 |
The first qfunctions | 194 |
qhypergeometric series | 241 |
Sundry topics | 279 |
467 | |
469 | |
471 | |
472 | |
477 | |
480 | |
483 | |
Notation index Chapter 3 | 485 |
qorthogonal polynomials | 309 |
qfunctions of several variables | 359 |
Linear partial qdifference equations | 427 |
qCalculus and physics | 441 |
447 | |
Notation index Chapter 4 5 | 486 |
Notation index Chapter 1011 | 488 |
Notation index Chapter 12 | 489 |