A Comprehensive Treatment of q-Calculus (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
492
Utgivningsdatum
2012-09-08
Upplaga
2012 ed.
Förlag
Birkhauser Verlag AG
Illustrationer
XVI, 492 p.
Dimensioner
234 x 157 x 33 mm
Vikt
726 g
Antal komponenter
1
Komponenter
1 Hardback
ISBN
9783034804301

A Comprehensive Treatment of q-Calculus

av Thomas Ernst
Inbunden,  Engelska, 2012-09-08
1505
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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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Innehållsförteckning

1 Introduction.- 2 The different languages of q.- 3 Pre q-Analysis.- 4 The q-umbral calculus and the semigroups. The Norlund 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.

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