| 1 Introduction | 第22-31页 |
| 1.1 A brief history | 第22-23页 |
| 1.2 Interpolation | 第23-26页 |
| 1.3 Orthogonal polynomials | 第26-29页 |
| 1.4 Gauss type quadrature rules | 第29-31页 |
| 2 Gauss-Radau Formulae and Gauss-Lobatto Formulae for Some Weight Functions | 第31-43页 |
| 2.1 Ganss-Radau formulae for the Jacobi and Laguerre weight functions | 第31-35页 |
| 2.2 Gauss-Lobatto formulae for the Jacobi weights | 第35-38页 |
| 2.3 Ganss-Radau formula and Gauss-Lobatto formula for the Gori and Micchelli weight function class | 第38-41页 |
| 2.4 Some remarks on Gaussian formulae for the four Chebyshev weights | 第41-43页 |
| 3 Gauss-Kronrod Quadrature Rules and Related Topics | 第43-63页 |
| 3.1 Stieltjes polynomials and their generalizations | 第45-53页 |
| 3.2 Extended Gaussian quadrature rules | 第53-57页 |
| 3.3 Some explicit extended Ganssian quadrature rules | 第57-61页 |
| 3.4 Kronrod extension of Gauss formulae as automatic integration | 第61-63页 |
| 4 Gauss-Turán Quadrature | 第63-82页 |
| 4.1 Fourier-Chebyshev coefficients and Gauss-Turán quadrature with Chebyshev weight | 第65-73页 |
| 4.1.1 Some auxiliary lemmas | 第70-72页 |
| 4.1.2 Proof of the theorem | 第72-73页 |
| 4.2 Other Known Ganss-Turán Quadrature rules | 第73-82页 |
| 4.2.1 Main Results | 第76-78页 |
| 4.2.2 Proofs of Theorems | 第78-82页 |
| 5 Other Gaussian Quadratures | 第82-96页 |
| 5.1 New quadrature formulas based on the zeros of the Chebyshev polynomials of the second kind | 第82-90页 |
| 5.1.1 Auxiliary lemmas | 第84-87页 |
| 5.1.2 Proofs of theorems | 第87-90页 |
| 5.2 Quadrature formulas for Fourier-Chebyshev coefficients | 第90-96页 |
| 5.2.1 Main results | 第90-91页 |
| 5.2.2 Auxiliary lemmas | 第91-93页 |
| 5.2.3 Proofs of theorems | 第93-96页 |
| A Numerical examples | 第96-105页 |
