Quadrature interpolation type formulas for hypersingular integrals in the interval of integration
L. Yu. Plieva1,2
1Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, str. Vatutina, 53, Vladikavkaz, Republic North Ossetia-Alania, 362027, Russia
2North Ossetian State University named after K.L. Hetagurov, str. Vatutina, 44, Vladikavkaz, Republic North Ossetia-Alania, 362025, Russia
Keywords: гиперсингулярный интеграл, квадратурная формула, оценка погрешности, hypersingular integral, quadrature formula, the estimation error
Abstract
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.
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