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Recurrence relations from modified moments for solutions fo certain integrals using Chebyshev polynomials. (English) Zbl 0844.65013

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
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