A Comprehensive Treatment of q-Calculus
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 theo...
में बचाया:
| मुख्य लेखक: | |
|---|---|
| स्वरूप: | Livre numérique |
| भाषा: | Anglais |
| प्रकाशित: |
Basel :
Springer Basel
[20..].
Cham : Springer Nature |
| संस्करण: | 1st ed. 2012. |
| ऑनलाइन पहुंच: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| टिप्पणी: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • A comprehensive treatment of q-calculus, Thomas Ernst, Basel, Birkhäuser, Springer, 2012, 1 vol. (XVI-491 p.), 978-3-0348-0430-1 |
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| 041 | 0 | |a eng | |
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| 100 | 1 | |a Ernst, Thomas, |d 1960-...., |c mathématicien. | |
| 245 | 1 | 0 | |a A Comprehensive Treatment of q-Calculus |c by Thomas Ernst. |
| 250 | |a 1st ed. 2012. | ||
| 260 | |a Basel : |b Springer Basel. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. Beyond a thorough review of the historical development of q-calculus, it 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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