Methods of Numerical Integration

a₁ abscissas abscissas and weights accuracy algorithm analytic applied approximate integration asymptotic automatic integration bounded c₁ CACM Cauchy principal value coefficients computed constants convergence defined derivatives differential equations Doncker dx dy endpoints error estimate Exact value example expansion f(x₁ finite fo f(x Fourier Transform function f functional evaluations Gauss rule Gaussian Gautschi given h₁ Hence improper integral indefinite integral infinite interval inner product integrand integration formula integration rule interpolation interpolatory Kronrod Krylov Laguerre linear Lyness M₁ method midpoint rule number of functional number of points numerical integration nx dx obtain orthogonal polynomials oscillatory quadrature Rabinowitz recurrence References Riemann integral Riemann sums Romberg roundoff Section sequence Simpson's rule singularity spline subintervals t₁ term THEOREM trapezoidal rule Tschebyscheff variable w₁ weight function x₁ Xi+1 zeros