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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Ernst, Thomas (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Springer Basel : Imprint: Birkhäuser, 2012.
Edición:1st ed. 2012.
Temas:
Special functions.
Number theory.
Special Functions.
Number Theory.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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