Geodesic
Trigonometric Gaussian quadrature on subintervals of the period
Electronic transactions on numerical analysis, Tome 39 (2012), pp. 102-112
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.
Classification : 65D32
Keywords: trigonometric Gaussian quadrature, subintervals of the period, product Gaussian quadrature, circular sectors, circular zones, circular segments, circular lenses 
@article{ETNA_2012__39__a19,
     author = {Da Fies,  Gaspare and Vianello,  Marco},
     title = {Trigonometric {Gaussian} quadrature on subintervals of the period},
     journal = {Electronic transactions on numerical analysis},
     pages = {102--112},
     year = {2012},
     volume = {39},
     zbl = {1287.65018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2012__39__a19/}
}
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Da Fies,  Gaspare; Vianello,  Marco. Trigonometric Gaussian quadrature on subintervals of the period. Electronic transactions on numerical analysis, Tome 39 (2012), pp. 102-112. http://geodesic.mathdoc.fr/item/ETNA_2012__39__a19/