Okecha, G. E. Recurrence relations from modified moments for solutions fo certain integrals using Chebyshev polynomials. (English) Zbl 0844.65013 J. Inst. Math. Comput. Sci., Math. Ser. 1, No. 1, 49-63 (1988). Summary: Recurrence relation formulae are derived from modified moments using Chebyshev polynomials for the numerical evaluation of the following integrals \(\int^1_{-1} \ln|x- \lambda|g(x) dx\), \(\lambda\in (- 1, 1)\); \(\int^1_{- 1} e^{i\omega x} g(x) dx\), \(\omega\ggg 1\); \(\int^1_{- 1} (x^2+ a^2)^\alpha g(x) dx\), \(\alpha> - 1\); \(\int^1_{- 1} (1+ x)^\alpha e^{- a(x+ 1)} g(x) dx\), \(\alpha> -1\); which are of practical importance in Engineering, Physics and Mathematics, and where \(a\) is a real or purely imaginary parameter. In particular, we examine the numerical stability of the recurrence relations occurring in this method. A numerical example is presented to illustrate the method. MSC: 65D32 Numerical quadrature and cubature formulas 65Q05 Numerical methods for functional equations (MSC2000) 41A55 Approximate quadratures Keywords:convergence; error bound; modified moments; Chebyshev polynomials; numerical stability; recurrence relations; numerical example PDFBibTeX XMLCite \textit{G. E. Okecha}, J. Inst. Math. Comput. Sci., Math. Ser. 1, No. 1, 49--63 (1988; Zbl 0844.65013)