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A Comprehensive Treatment of q-Calculus / by Thomas Ernst.

Por: Colaborador(es): Tipo de material: TextoTextoEditor: Basel : Springer Basel : Imprint: Birkhäuser, 2012Descripción: xvI, 495 páginas 15 ilustraciones, 1 ilustraciones en color. recurso en líneaTipo de contenido:
  • texto
Tipo de medio:
  • computadora
Tipo de portador:
  • recurso en línea
ISBN:
  • 9783034804318
Formatos físicos adicionales: Edición impresa:: Sin títuloClasificación LoC:
  • QA351
Recursos en línea:
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.
Resumen: 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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Springer eBooks

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.

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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