Handbook of Computational Methods for Integration

ISBN: 9780367393458 出版年：2004 页码：621 Kythe, Prem K CRC Press

Preface Notation Preliminaries Notation and Definitions Orthogonal Polynomials Finite and Divided Differences Interpolation Semi-Infinite Interval Convergence Accelerators Polynomial Splines Interpolatory Quadrature Riemann Integration Euler-Maclaurin Expansion Interpolatory Quadrature Rules Newton-Cotes Formulas Basic Quadrature Rules Repeated Quadrature Rules Romberg's Scheme Gregory's Correction Scheme Interpolatory Product Integration Iterative and Adaptive Schemes Test Integrals Gaussian Quadrature Gaussian Rules Extended Gaussian Rules Other Extended Rules Analytic Functions Bessel's Rule Gaussian Rules for the Moments Finite Oscillatory Integrals Noninterpolatory Product Integration Test Integrals Improper Integrals Infinite Range Integrals Improper Integrals Slowly Convergent Integrals Oscillatory Integrals Product Integration Singular Integrals Quadrature Rules Product Integration Acceleration Methods Singular and Hypersingular Integrals Computer-Aided Derivations Fourier Integrals and Transforms Fourier Transforms Interpolatory Rules for Fourier Integrals Interpolatory Rules by Rational Functions Trigonometric Integrals Finite Fourier Transforms Discrete Fourier Transforms Hartley Transform Inversion of Laplace Transforms Use of Orthogonal Polynomials Interpolatory Methods Use of Gaussian Quadrature Rules Use of Fourier Series Use of Bromwich Contours Inversion by the Riemann Sum New Exact Laplace Inverse Transforms Wavelets Orthogonal Systems Trigonometric System Haar System Other Wavelet Systems Daubechies' System Fast Daubechies Transforms Integral Equations Nystrom System Integral Equations of the First Kind Integral Equations of the Second Kind Singular Integral Equations Weakly Singular Equations Cauchy Singular Equations of the First Kind Cauchy Singular Equations of the Second Kind Canonical Equation Finite-Part Singular Equations Integral Equations Over a Contour Appendix A: Quadrature Tables Cotesian Numbers, Tabulated for kGBPn/2, n=1(1)11 Weights for a Single Trapezoidal Rule and Repeated Simpson's Rule Weights for Repeated Simpson's Rule and a Single Trapezoidal Rule Weights for a Single 3/8-Rule and Repeated Simpson's Rule Weights for Repeated Simpson's Rule and a Single 3/8-Rule Gauss-Legendre Quadrature Gauss-Laguerre Quadrature Gauss-Hermite Quadrature Gauss-Radau Quadrature Gauss-Lobatto Quadrature Nodes of Equal-Weight Chebyshev Rule Gauss-Log Quadrature Gauss-Kronrod Quadrature Rule Patterson's Quadrature Rule Filon's Quadrature Formula Gauss-Cos Quadrature on [pi/2, pi/2] Gauss-Cos Quadrature on [0, pi/2] Coefficients in (5.1.15) with w(x)=ln(1/x), 0