Details
A Comprehensive Treatment of q-Calculus
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96,29 € |
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| Verlag: | Birkhäuser |
| Format: | |
| Veröffentl.: | 13.09.2012 |
| ISBN/EAN: | 9783034804318 |
| Sprache: | englisch |
| Anzahl Seiten: | 495 |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<p>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.</p><p>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. </p>
1 Introduction.- 2 The different languages of q.- 3 Pre q-Analysis.- 4 The q-umbral calculus and the semigroups. The Nørlund calculus of finite diff.- 5 q-Stirling numbers.- 6 The first q-functions.- 7 An umbral method for q-hypergeometric series.- 8 Applications of the umbral calculus.- 9 Ciglerian q-Laguerre polynomials.- 10 q-Jacobi polynomials.- 11 q-Legendre polynomials and Carlitz-AlSalam polynomials.- 12 q-functions of many variables.- 13 Linear partial q-difference equations.- 14 q-Calculus and physics.- 15 Appendix: Other philosophies.
<p>To date, the theoretical development of <i>q</i>-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on <i>q</i>-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 <i>q</i>-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for <i>q</i>-calculus based on logarithms. For instance, <i>q</i>-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 <i>q</i>-hypergeometric functions and the <i>q</i>-gamma function, something that until now has been overlooked.<br><br>The book covers many topics on <i>q</i>-calculus, including special functions, combinatorics, and <i>q</i>-difference equations. Beyond a thorough review of the historical development of <i>q</i>-calculus, it also presents the domains of modern physics for which <i>q</i>-calculus is applicable, such as particle physics and supersymmetry, to name just a few.</p>
<p>Covers many topics on q-calculus, i.e. special functions, combinatorics, q-difference equations and q-Bernoulli numbers</p><p>Detailed coverage of the historical development of q-calculus</p><p>Summarizes the domains of moderns physics for which q-calculus is applicable, i.e. particle physics and supersymmetry</p><p>Introduction of a new logarithmic notation for q-calculus that supersedes the older Gaspar-Rahman notation</p><p>Includes supplementary material: sn.pub/extras</p>
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