The aim of this paper is to give many new and interesting identities, relations, and combinatorial sums including the Hermite-based Milne-Thomson type polynomials, the Chebyshev polynomials, the Fibonacci-type polynomials, trigonometric type polynomials, the Fibonacci numbers, and the Lucas numbers. By using Wolfram Mathematica version 12.0, we give surfaces graphics and parametric plots for these polynomials and generating functions. Moreover, by applying partial derivative operators to these generating functions, some derivative formulas for these polynomials are obtained. Finally, suitable connections of these identities, formulas, and relations of this paper with those in earlier and future studies are designated in detail remarks and observations.

中文翻译：

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与斐波那契和切比雪夫多项式相关的基于 Hermite 的 Milne-Thomson 多项式的恒等式和关系

本文的目的是给出许多新的有趣的恒等式、关系和组合和，包括基于 Hermite 的 Milne-Thomson 型多项式、Chebyshev 多项式、Fibonacci 型多项式、三角型多项式、Fibonacci 数和卢卡斯数字。通过使用 Wolfram Mathematica 12.0 版，我们为这些多项式和生成函数提供了曲面图形和参数图。此外，通过对这些生成函数应用偏导数算子，得到了这些多项式的一些导数公式。最后，在详细的评论和观察中指定了本文的这些恒等式、公式和关系与早期和未来研究中的这些恒等式、公式和关系的适当联系。