Geodesic
Quadrature interpolation type formulas for hypersingular integrals in the interval of integration
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 4, pp. 419-428

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A hypersingular integral on the interval of integration with the weight function is considered. We prove the spectral ratios for hypersingular integrals on $[-1,1]$. The quadrature formulas for certain integrals with the weight function are constructed. The estimation error is presented. 
@article{SJVM_2016_19_4_a5,
     author = {L. Yu. Plieva},
     title = {Quadrature interpolation type formulas for hypersingular integrals in the interval of integration},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {419--428},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2016_19_4_a5/}
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L. Yu. Plieva. Quadrature interpolation type formulas for hypersingular integrals in the interval of integration. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 4, pp. 419-428. http://geodesic.mathdoc.fr/item/SJVM_2016_19_4_a5/