A blend of two Taylor series for the same smooth real- or complex-valued function of a single variable can be useful for approximation. We use an explicit formula for a two-point Hermite interpolational polynomial to construct such blends. We show a robust Maple implementation that can stably and efficiently evaluate blends using linear-cost Horner form, evaluate their derivatives to arbitrary order at the same time, or integrate a blend exactly. The implementation is suited for use with evalhf. We provide a top-level user interface and efficient module exports for programmatic use. This work intended for presentation at the Maple Conference 2020. See www.maplesoft.com/mapleconference

中文翻译：

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混合枫木

将两个泰勒级数混合用于单个变量的相同平滑实值或复值函数可用于逼近。我们使用两点 Hermite 插值多项式的显式公式来构造这种混合。我们展示了一个健壮的 Maple 实现，它可以使用线性成本霍纳形式稳定有效地评估混合，同时将它们的导数评估为任意顺序，或者精确地整合混合。该实现适合与 evalhf 一起使用。我们提供顶级用户界面和高效的模块导出以供编程使用。这项工作旨在在 Maple Conference 2020 上进行展示。请参阅 www.maplesoft.com/mapleconference