COMPUTING THE COEFFICIENTS OF A RECURRENCE FORMULA FOR NUMERICAL-INTEGRATION BY MOMENTS AND MODIFIED MOMENTS

To evaluate the class of integrals integral-1/-1 e(-alphax)f(x) dx, where alpha is-an-element-of R+ and the function f(x) is known only approximately in a tabular form, we wish to use a Gaussian quadrature formula. Nodes and weights have to be computed using the family of monic orthogonal polynomials, with respect to the weight function e(-alphax), obtained through the three-term recurrence relation P(k+1)(x) = (x + B(k+1)P(k)(x) - C(k+1)P(k-1)(x). To guarantee a good precision, we must evaluate carefully the values for the coefficients B(k+1) and C(k+1). Such evaluations are made completely formally through a Mathematica program to obtain great precision. A comparison between various methods, starting from moments and modified moments; is shown. Numerical results are also presented.