A Comprehensive Treatment of q-Calculus

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Springer Science & Business Media, 8 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.

 

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Continguts

Introduction
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

qorthogonal polynomials
309
qfunctions of several variables
359
Linear partial qdifference equations
427
qCalculus and physics
441
References
447
Notation index Chapter 4 5
486
Notation index Chapter 1011
488
Notation index Chapter 12
489
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