7 Orthogonal polynomial sequences

Chapters in this book

1. Frontmatter I
2. Preface VII
3. Contents XI
4. Part I: Basic methods
5. Introduction 1
6. 0 Infinite lower triangular matrices and formal power series 5
7. 1 Polynomial sequences: algebraic structure, recurrence and determinant form, operational methods 56
8. 2 Symmetric polynomial sequences 97
9. 3 Generating functions 117
10. 4 Differential operator and Sheffer classification 129
11. 5 The monomiality principle 143
12. Part II: Special classes of polynomial sequences
13. Introduction 155
14. 6 Sheffer polynomial sequences 157
15. 7 Orthogonal polynomial sequences 207
16. 8 Lidstone and central factorial-type polynomial sequences 238
17. 9 Bernstein basis 293
18. 10 Bivariate special polynomials: hints 310
19. Part III: Computational applications
20. Introduction 359
21. 11 Approximation theory by operators 361
22. 12 Interpolation 390
23. 13 Boundary value problems and polynomial sequences 430
24. 14 Appell and Lidstone-type quadrature formulas 463
25. Postface 485
26. Bibliography 487
27. Index 503