Volume 39, pp. 102-112, 2012.

Trigonometric Gaussian quadrature on subintervals of the period

Gaspare Da Fies and Marco Vianello


We construct a quadrature formula with $n+1$ angles and positive weights which is exact in the $(2n+1)$-dimensional space of trigonometric polynomials of degree $\leq n$ on intervals with length smaller than $2\pi$. We apply the formula to the construction of product Gaussian quadrature rules on circular sectors, zones, segments, and lenses.

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Key words

trigonometric Gaussian quadrature, subintervals of the period, product Gaussian quadrature, circular sectors, circular zones, circular segments, circular lenses

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