- 176 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Classical Orthogonal Polynomials, The
About this book
This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have.
The first chapter defines the orthogonality condition for two functions. It then gives an iterative process to produce a set of polynomials which are orthogonal to one another and then describes a number of properties satisfied by any set of orthogonal polynomials. The classical orthogonal polynomials arise when the weight function in the orthogonality condition has a particular form. These polynomials have a further set of properties and in particular satisfy a second order differential equation.
Each subsequent chapter investigates the properties of a particular polynomial set starting from its differential equation.
This book defines sets of orthogonal polynomials and derives a number of properties satisfied by any such set. It continues by describing the classical orthogonal polynomials and the additional properties they have.
The first chapter defines the orthogonality condition for two functions. It then gives an iterative process to produce a set of polynomials which are orthogonal to one another and then describes a number of properties satisfied by any set of orthogonal polynomials. The classical orthogonal polynomials arise when the weight function in the orthogonality condition has a particular form. These polynomials have a further set of properties and in particular satisfy a second order differential equation.
Each subsequent chapter investigates the properties of a particular polynomial set starting from its differential equation.
Readership: Undergraduate and graduate students.
Frequently asked questions
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app
Information
Table of contents
- Cover Page
- Title Page
- Copyright
- Contents
- Preface
- 1. Definitions and General Properties
- 2. Hermite Polynomials
- 3. Associated Laguerre Polynomials
- 4. Legendre Polynomials
- 5. Chebyshev Polynomials of the First Kind
- 6. Chebyshev Polynomials of the Second Kind
- 7. Chebyshev Polynomials of the Third Kind
- 8. Chebyshev Polynomials of the Fourth Kind
- 9. Gegenbauer Polynomials
- 10. Associated Legendre Functions
- 11. Jacobi Polynomials
- 12. General Appendix
- Index