Abstract A dozen families of integer–valued polynomials arising in finite summation of various trigonometric sums are known and all of them were deduced through numerical analysis methods. Here, using simple arguments commonly applied in work with polynomial sequences, we examined such expressions in full detail as well as in a systematic and unified manner. Two new very general integer–valued polynomial families (along with six other families derived from them, also integer–valued, including three previously studied) were obtained and they are related to each other by a binomial transform of sequences and associated with certain cosecant and cotangent sums.

中文翻译：

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与有限三角和相关的两个整数值多项式的一般族

摘要 已知各种三角和的有限求和所产生的十多族整数值多项式，它们都是通过数值分析方法推导出来的。在这里，我们使用通常应用于多项式序列的简单参数，以系统和统一的方式全面详细地检查了这些表达式。获得了两个新的非常普遍的整数值多项式族（以及从它们派生的其他六个族，也是整数值的，包括先前研究的三个），它们通过序列的二项式变换相互关联，并与某些余割和余切和。