The evaluation and application of some modified moments |
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Authors: | Robert Piessens Maria Branders |
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Institution: | 1. Applied Mathematics and Programming Division, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3030, Heverlee, Belgium
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Abstract: | Recurrence formulas for the calculation of the modified moments $$\int\limits_{ - 1}^{ + 1} {(1 - x)^\alpha (1 + x)^\beta T_n (x)dx} $$ and $$\int\limits_{ - 1}^{ + 1} {(1 - x)^\alpha (1 + x)^\beta \ln \left( {\frac{{1 + x}}{2}} \right)T_n (x)dx} $$ are presented. Some applications of these modified moments are discussed, such as the numerical calculation of integrals of functions having branch points, the computation of Chebyshev series coefficients and the construction of Gaussian quadrature formulas for integrals with logarithmic singularity. |
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