دانلود کتاب On the Higher-Order Sheffer Orthogonal Polynomial Sequences
by Daniel J. Galiffa
|
عنوان فارسی: در مرتبه بالاتر دنباله های چند جمله ای متعامد شفر |
دانلود کتاب
جزییات کتاب
Table of Contents
Cover
On the Higher-Order Sheffer Orthogonal Polynomial Sequences
ISBN 9781461459682 ISBN 9781461459699
Preface
Contents
The Sheffer A-Type 0 Orthogonal Polynomial Sequences and Related Results
1.1 Preliminaries
1.2 Sheffer's Analysis of the Type 0 Polynomial Sequences
1.3 The Type 0 Orthogonal Polynomials
1.4 An Overview of the Classification of Type
1.4.1 The Sheffer A-Type Classification
1.4.2 The Sheffer B-Type Classification
1.4.3 The Sheffer C-Type Classification
1.4.4 A Summary of the Rainville s-Type Classifiation
1.5 A Brief Discussion of Meixner's Analysis
1.5.1 Al-Salam's Extension of Meixner's Characterization
Some Applications of the Sheffer A-Type 0 Orthogonal Polynomial Sequences
2.1 Preliminaries
2.2 Differential Equations Part I: The "Inverse Method"
2.3 Differential Equations Part II
2.4 Difference Equations
2.5 Gaussian Quadrature
2.6 Problems
A Method for Analyzing a Special Case of the Sheffer B-Type 1 Polynomial Sequences
3.1 Preliminaries
3.2 The Formulation of Our Main Problem
3.3 The B-Type 1 Recursion Coeffcients
3.4 Lower-Order B-Type 1 Polynomials Obtained via Generating Function
3.5 Lower-Order B-Type 1 Polynomials Obtained via Three-Term Recurrence Relation
3.6 Managing the Complexity of the Sheffer B-Type 1 Class
3.7 The Solutions of the Simultaneous, Nonlinear, Algebraic System
3.8 On the Verification of Solutions via Computer Algebra
3.9 Conclusion and Future Considerations