In this paper we consider some applications of Odd and Even Lidstone-type polynomial sequences. In particular we deal with the Odd and Even Lidstone-type and the Generalized Lidstone interpolatory problems with respect to a linear functional \(L_1\) and, respectively, \(L_2\). Estimations of the remainder for the related interpolation polynomials are given. Numerical examples are provided. Some possible applications of these interpolant polynomials to BVPs, expansions of analytical real functions and numerical quadrature are sketched.

中文翻译：

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奇偶数Lidstone型多项式序列。第2部分：应用

在本文中，我们考虑奇数和偶数Lidstone型多项式序列的一些应用。特别是，我们分别处理线性函数\（L_1 \）和\（L_2 \）的奇偶偶数Lidstone型和广义Lidstone插值问题。给出了相关插值多项式的余数估计。提供了数值示例。这些插值多项式对BVP的一些可能应用，解析实函数的扩展和数值正交。