A Comprehensive Treatment of q-Calculus

• Κύριος συγγραφέας: Ernst, Thomas (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Springer Basel : Imprint: Birkhäuser, 2012.
• Θέματα: Mathematics.; Special functions.; Number theory.; Special Functions.; Number Theory.

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...

Πίνακας περιεχομένων:

• 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.