Abstract: A quantitative estimates in the theory of equiconvergence of differences between the Hermite interpolant and Jacobi polynomials is obtained for functions analylic inside lemniscate. A necessary and sufficient condition that the related difference converges uniformly to zero on the boundary of the equiconvergence area is also showed.

Key words: Jacobi expansion, Hermite interpolant, equiconvergence

摘要： 对纽线内部的解析函数，得到了Hermite插值与Jacobi多项式之差的过收敛性的精确估计；此外还指出有关的差在过收敛区域的边界上一致收敛的充分必要条件。

关键词: Jacobi展开, Hermite插值, 过收敛性