On Paratrigonometric Lagrange Interpolation And Its Application In Singular Integral Equation With Cosecant Kernel

The interpolation is an important content of function approximation. The results about the polynomial Lagrange interpolation and the Hermite interpolation have been completed; there are also many achievements about trigonometrical function Lagrange interpolation and its applications.Compared with those achievements the result of approaching the 2n counter-periodic function with paratrigonometrical function Lagrange interpolation is relatively less. When the number of interpolation nodes is even, paratriangle Lagrange interpolation question is suitably decided. When the number of interpolation nodes is odd, paratriangle Lagrange interpolation question is not suitably decided. The conclusions above have the essential distinction with the polynomial Lagrange interpolation. In the second chapter in this article, we have produced paratriangle Lagrange interpolation question and the construct interpolation basic functions; When the interpolated function have some analytic character,we have gived integral expression of paratriangle Lagrange interpolating function and the interpolation remainder. In the third chapter, we have clarified some views about the quadrature formula triangle precision in the teachingmaterial,and pointed out the difference between the triangle precision and the algebra precision. Also we used the results of the quadrature formula of periodic function and paratriangle Lagrange interpolation to study a kind of singular integral with cosecant kernel the singular integral value quadrature method, and finally we have established the corresponding quadrature formula and produced the paratriangle precision. In charpter four,we...